# ma: A Pathfinder

This is a computer-generated pathfinder created against the Distant Reader study called ma.

Each Distant Reader study carrel is composed of many individual items. Each item is bibliographically described with author, title, date, summary, and keyword values. Below is a list of the items' most signficant keywords as well as lists of the items themselves. Purpusing the content of this pathfinder provides the student, researcher, or scholar with one way to get their heads around the scope of the carrel. The keywords include:

> Convergence; Method; Anal; Model; Lim; Order; I=1; Ada; Operator; Equation; Theorem; Fractional; System; Norm; Graph; Convex; Disease; Frame; Scheme; I=0; Data; Inequality; I∈[m; Θ̃t; Eθt; L1ω(g; Y‖2; 2πi; B∞,; Inequalities; Curve; A∗η; Logq; Lp)α; S(z; Liouville; Solution; K=1; Sequences; R+q; Dνα; Variable; Γ(α2; J(ρ; Αq‖2; 0(ω; C∗-algebra; Orthogonality

Depending on how this pathfinder was created, many of the bibliographic sections will include elaborations on the meaning(s) of the given keywords. These elaborations were generated by feeding the items' summaries to a large langauge model and asking the model to address the question, "What is X?", where "X" is the keyword. The result will be a few sentences of elaboration. Be forewarned. The elaborations are often plausible, but they should not be take as truth. Instead, they should be taken as points for consideration.

## Convergence

- Updated and Weaker Convergence Criteria of Newton Iterates for Equations by Regmi, Samundra; Argyros, Ioannis K.; George, Santhosh ; Argyros, Michael I. (2022) - − xi+1‖ ≤ ‖v − xi+2‖+ ‖xi+2 − xn‖ ≤ s∗ − sn (3.1) hold ∀n = 0, 1, 2, . . . . Keywords: anal; convergence
- Developments on the Convergence Analysis of Newton-Kantorovich Method for Solving Nonlinear Equations by Regmi, Samundra; Argyros, Ioannis K.; George, Santhosh ; Argyros, Michael I. (2023) - − xn‖ ≤ s∗ − sn, (2.19) where, limn−→∞ sn = s∗ = 1− √ 1−2H Kα and s∗∗ = 1+ √ 1−2H Kα . − tn (2.23) and 0 ≤ s∗ − sn ≤ t∗ − tn. Keywords: convergence; newton
- Unified Convergence Analysis of Two-Step Iterative Methods for Solving Equations by Argyros, Ioannis K. (2021) - − x∗‖)‖xm − x∗‖ ≤ ‖xm − x∗‖ < R (4.10)and ‖xm+1 − x∗‖ ≤ ψ2(‖xm − x∗‖)‖xm − x∗‖ ≤ ‖xm − x∗‖. (4.11)Then, by the estimation ‖xm+1 − x∗‖ ≤ d‖xm − x∗‖ < R, (4.12)where d = ψ2(‖x0 − x∗‖) ∈ = yn − F ′(xn)−1F (yn), (1.3) Newton Keywords: convergence; math
- Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations by Kumar, Sunil ; Sharma, Janak Raj ; Argyros, Ioannis K.; Regmi, Samundra (2023) - Consequently, we have ‖xn+1 − zn‖ ≤ β̄n(1 + w0(‖yn − x0‖, ‖zn − x0‖))‖zn − yn‖ 1− w0(f1(‖xn = (I + L+ LL−1([xn, x ∗;F ]− L))(xn − x∗), so ‖un − x∗‖ ≤ ( ‖I + L‖+ (‖L‖w(‖(xn − x∗)‖)) ) ‖(xn − x∗)‖.Thus, we can choose f1(t) Keywords: convergence; math; method; − x0‖; − x∗‖
- Efficient Derivative-Free Class of Seventh Order Method for Non-differentiable Equations by Argyros, oannis K.; Regmi, Samundra; John, Jinny Ann ; Jayaraman, Jayakumar (2023) - ≤ 1 1− ϕ0(δ1(‖xn − ξ‖), δ2(‖xn − ξ‖)) , yn − ξ = A−1n (An − [xn, ξ;G])(xn − ξ), ‖yn − ξ‖ ≤ ϕ(‖xn − ξ‖, ‖wn − ξ‖, ‖sn − ξ‖)‖xn − ξ‖ 1− ϕ0(δ1(‖xn − ξ‖), δ2(‖xn − ξ‖)) ≤ h1(‖xn − ξ‖)‖xn − ξ‖ ≤ ‖xn − ξ‖ < r. Similarly, ‖zn − ξ‖ ≤ ϕ(‖yn − ξ‖, ‖wn − ξ‖, ‖sn − ξ‖)‖yn − ξ‖ 1− ϕ0(δ1(‖xn − ξ‖), δ2(‖xn − ξ‖)) ≤ h2(‖xn − ξ‖)‖xn − ξ‖ ≤ ‖xn − ξ‖, xn+1 − ξ = zn − ξ − A−1n G(zn)− [(p + q + r + d − 1)I + (q + 2r + 3d)(A−1n Keywords: convergence; math; method; order; − x0‖
- Two Point Iterative Schemes for Nondifferentiable Equations in Banach Space by Argyros, Ioannis K.; Joshi, Janak; Regmi, Samundra (2023) - Then, by the scheme (1.2) for n replaced by n + 1, we obtain: ‖xn+2 − xn+1‖ ≤ ‖A(xn+1, xn)−1P‖‖PF (xn+1)‖ ≤ v(γn+1 − γn, γn − γn−1) 1− v0(‖xn+1 − x0‖, ‖xn − x0‖) ≤ v(γn+1 − γn, γn − γn−1)(γn+1 − γn) 1− v0(γn+1, γn)and ‖xn+2 − x0‖ ≤ ‖xn+2 x1 − x∗ = x0 − x∗ − A(x0 − x−1)−1F (x0) Keywords: convergence; scheme; x∗‖
- A Unified Kantorovich-type Convergence Analysis of Newton-like Methods for Solving Generalized Equations under the Aubin Property by Regmi, Samundra; Argyros, Ioannis K.; George, Santhosh; Warden, Jefferey (2024) - − L(xm)‖‖v1 − v2‖ ≤ w0(‖xm − x0‖)‖v1 − v2‖ ≤ w0(ρ)‖v1 − v2‖, where w0(ρ) < 1, by the definition of ρ. − xm‖ 1 λ [∫ 1 0 w0((1− θ)‖x − x0‖)dθ‖x − x0‖ + ∫ 1 0 w((1− θ)‖x − xm‖)dθ‖x − xm‖ +w0(‖xm − x0‖)‖x − xm‖+ w1)‖xm − x0‖)‖x − xm‖] ≤ 1 λ [∫ 1 0 w0((1− θ)ρ)dθ + w0(ρ) Keywords: convergence; method; newton
- Schwarz Algorithms for Stokes-Stokes Coupling by Kyriakis, Alexandros (2025) - References [1] M.J. Gander, Optimized Schwarz methods for Helmholtz problems, in: Proceedings of the 13th International Con-ference on Domain Decomposition, CIMNE (2001) 245-252.[2] M.J. Gander, L. Halpern, F. Nataf, Optimized Schwarz methods, in: Proceedings of the 12th International Conferenceon Domain Decomposition, ddm.org (2000) 15-27.[3] P.L. Lions, On the Schwarz alternating method III: A variant for nonoverlapping subdomains, in: T. Chan, R. Glowinski,J. Periaux, O.B. Widlund (Eds.), Third International Symposium on Domain Decomposition Methods for PartialDifferential Equations, SIAM (1990) 202-223.[4] M.J. Gander, G. Wanner, The origins of the alternating Schwarz method, in: Domain Decomposition Methods inScience and Engineering XXI, LNCSE, Springer-Verlag (2014) 487-496.[5] M.J. Gander, Schwarz methods over the course of time, Elec. Convergence rate of Schwarz method using Dirichlet IC for varying overlap. Keywords: convergence; fourier; methods; schwarz
- Hybrid Iterative Methods for Solving Nonlinear Equations in Banach Spaces by Argyros, Ioannis K.; George, Santhosh; Regmi, Samundra; Argyros, Michael I. (2025) - − s∗))‖ ≤ φ(‖s∗ − x0‖, ‖w − x0‖, ‖w − s∗‖)‖w − s∗‖ ≤ φ(α∗, α∗, ‖w − s∗‖)‖w − s∗‖ < ‖w − s∗‖, which gives a contradiction. − s∗‖)‖w1 − s∗‖ < ‖w1 − s∗‖ (2.12) by the choice of r . Keywords: anal; convergence; math; method; newton; operator
- Three Step Inverse Free Kurchatov-Like Methods of Convergence Order Close to Four for Equations by Argyros, Ioannis K.; Shakhno, Stepan; Yarmola, Halyna; Regmi, Samundra; Shrestha, Nirjal (2025) - − x∗ = xi − x∗ − Ti(F (xi)− F (x∗)) (2.10)We need the estimate ‖Ki+1 − F ′(xi)‖ = ‖[2yi − xi , xi ;F ]− [xi , xi ;F ]‖ ≤ l(‖2yi − xi − xi‖+ ‖xi − xi‖) Keywords: convergence; method
- On Local and Semi-Local Convergence Analysis of A High-Order Iterative Method for Solving Nonlinear Systems Without High Derivatives by Argyros, Ioannis K.; Shakhno, Stepan; Shunkin, Yurii; Regmi, Samundra; Argyros, Christopher I. (2025) - (2)n − x∗‖ ≤ g2(‖xn − x∗‖)‖xn − x∗‖ ≤ ‖xn − x∗‖, (13) ‖y (j)n − x∗‖ ≤ gj(‖xn − x∗‖)‖xn − x∗‖ ≤ ‖xn − x∗‖, (14) · · · https://doi.org/10.28924/ada/ma.5.18 Eur. J. Math. 10.28924/ada/ma.5.18 6 ‖xn+1 − x∗‖ = ‖y (k)n − x∗‖ ≤ gk(‖xn − x∗‖)‖xn − x∗‖ ≤ ‖xn − x∗‖. (15) Keywords: convergence; math; method; order; x∗‖
- On the Ostrowski Method for Solving Equations by Argyros, Ioannis K.; George, Santhosh ; Argyros, Christopher I. (2021) - For each x, y ∈ Ω0 ‖F ′(x0)−1(F ′(y)− F ′(x))‖ ≤ K‖y − x‖, ‖F ′(x0)−1([y , x ;F ]− F ′(x0))‖ ≤ K1(‖y ′(x∗)−1(A0 − F ′(y0))‖‖A−10 F ′(x∗)‖‖F ′(x∗)−1F (y0)‖ ≤ L‖y0 − x∗‖2 2(1− L0‖x0 − x∗‖ + (L2 + L3)‖y0 − x0‖L4‖y0 − x∗‖ (1− L0‖y0 − x∗‖)(1− p(‖x0 − x∗‖)) ≤ ϕ2(‖x0 − x∗‖)‖x0 − x∗‖ ≤ ‖x0 − x∗‖ < r, so x1 ∈ U(x∗, r), where we also used ‖F ′(x∗)−1(A0 − F ′(y0))‖ ≤ ‖F ′(x∗)−1([y0, x0;F ]− F ′(x0))‖ +‖F ′(x∗)−1([y0, x0;F ]− F ′(y0))‖ ≤ (L2 + L3)‖y0 − x0‖ ≤ (L2 + L3)(‖y0 − x∗‖+ ‖x0 − x∗‖) ≤ (L2 + L3)(1 + ϕ1(‖x0 − x∗‖))‖x0 − x∗‖, and ‖F ′(x∗)−1F (y0)‖ = ‖ ∫ 1 0 F ′(x∗) Keywords: convergence; math; method; x∗‖
- On the Semi-Local Convergence of a Third Order Scheme for Solving Nonlinear Equations by Regmi, Samundra; Argyros, Ioannis K.; George, Santhosh ; Argyros, Christopher (2022) - − F ′ ( xk + 3yk 4 ) ), (3.13) so ‖F ′(x0)−1 ∫ 1 0 (F ′(xk + θ(xk+1 − xk))dθ − 1 3 Mk)‖ ≤ K [ ‖xk+1 − xk‖ 2 + ‖yk − xk‖ 6 + ‖yk − xk‖ 4 + ‖yk − xk‖ 12 ] ≤ K( tk+1 − tk 2 + sk − tk 6 + sk − tk 4 + sk − tk 12 ) = ∫ 1 0 (F ′(xk + θ(xk+1 − xk))dθ − 1 3 Mk)(xk+1 − xk). Keywords: convergence; math

## Method

- Numerical Results for Gauss-Seidel Iterative Algorithm Based on Newton Methods for Unconstrained Optimization Problems by Dung, Nguyen Dinh (2025) - So, in this paper, we propose Gauss – Seidel algorithmsimplemented for the Newton and quasi-Newton method for finding solutions at each iterationstep, in which we inherit the information of the component solutions calculated in the current https://doi.org/10.28924/ada/ma.5.9 Eur. The calculation results show thatthe quasi-Newton method has the advantage of not requiring a quadratic differentiable objectivefunction, but the convergence is quite slow compared to the Newton method. Keywords: algorithm; method; newton; x(k

## Anal

- Analysis of Neuronal Oscillations of Fractional-Order Morris-Lecar Model by Azizi, Tahmineh (2022) - Figures (10)-(14),demonstrate the appearance and disappearance of saddle-homoclinic bifurcation in the model (13)with increasing the applied current Iapp = 23, 40, 50, 60, 70 like the original model (6) but liketwo previous bifurcations, for fractional order model of orders η = 0.3, .0.5, 0.7, 0.9 the neuronneeds higher input current Iapp to bifurcate. Because the solutions of fractional Morris Lecar model (FML) may not be explicitly obtained, weuse numerical methods to approximate the solutions of this model. Keywords: ada; anal; bifurcation; current; eur; fractional; https://doi.org/10.28924/ada/ma.3.2; iapp; lecar; math; model; morris; order
- Global Analysis of a Spatiotemporal Cellular Model for the Transmission of Hepatitis C Virus With Hattaf-Yousfi Functional Response by Nangue, Alexis; Tchiffo, Bruno Nde (2021) - [ dH∗ + αI∗ − dH − (1− η)βHV (1 + α1H)(1 + α2V ) + ρI ] − I∗ I (1− η) (1+α1H ∗)(1+α2V ∗)(α+ρ)I∗ (1−η)H∗V ∗ HV (1 + α1H)(1 + α2V ) − (α+ ρ)I − (α+ ρ)I V ∗ V + (α+ ρ)µ (1− ε)k V ∗, = [ dH∗ + (α+ ρ)I∗ − ρI∗ − dH − αI − (α+ ρ)I∗ V V ∗ ] − [H∗ H 1 + α1H 1 + α1H∗ dH∗ + H∗ H 1 + α1H 1 + α1H∗ αI∗ − 1 + α1H 1 + α1H∗ dH∗ − V V ∗ 1 + α2V ∗ 1 + α2V (α+ ρ)I∗ + H∗ H 1 + α1H 1 + α1H∗ ρI ] + (α+ ρ)I∗ [ 1− HI∗V (1 + α1H ∗)(1 + α2V ∗) Then, the computation of the derivative of G2 with respect to t yields : dG2 dt = [ λ− dH − αI − (α+ ρ)µ (1− ε)k V ] − (α+ ρ)I∗ (1 + α1H)(1 + α2V ∗) (1− η)βHV ∗ [ λ− dH − (1− η)βHV (1 + α1H)(1 + α2V ) + ρI ] − I∗ I Keywords: ada; anal; eur; hcv; https://doi.org/10.28924/ada/ma.3.1; infection; math; max; model; sup; system; α2v
- Modified Viscosity Iterative Algorithm for Solving Variational Inclusion and Fixed Point Problems in Real Hilbert Space by Mendy, Furmose; Mendy, John T (2024) - PKΘ‖ ≤ ‖[I + (α0γf − ηα0B)]x − ([I + (α0γf − ηα0B)]y)‖ ≤ α0γ‖f (x)− f (y)‖+ ‖(I − ηα0B)x − (I − ηα0B)y‖ ≤ α0γρ‖x − y‖+ (I − ατ)‖x − q‖2 + (1− βn)‖un − q‖2 − (1− βn)βn‖un − yn‖2 ≤ βn‖yn Keywords: anal; lim; math; xn)−; − q‖2
- Global Analysis of Meningitis Disease With Optimal Control by Danquah, Kwame Kyei; Appiah, Sampson Takyi; Danquah, Baaba A.; Afful, Bernard Asamoah; Safo, Godfred Agyemang (2024) - − k1τ1EHh − (1− k1)τ1EHh − µEHh, d dt AHh = (1− k1)τ1EHh − (τ2 + τ3 + µ)AHh, (1) It was seen that the most sensitiveparameters on R0 are Λ, τ1, ψ1, η1, k1, µ, and ψ2.An optimal control model was formulated by adding time-dependent optimal controls. Keywords: ahh; anal; asymptomatic; control; days; disease; ehh; graph; ihh; math; meningitis; model; rhh; shh; time
- Parameter Estimation for SPDEs Driven by Cylindrical Stable Processes by Bishwal, Jaya P. N. (2022) - as T →∞.c) T (α−1)/α2 (θ̂k,T − θ)→D ( σ2 k ν2 k )1/α S4 S3 as T →∞ where S4 and S3 are independent stable random variables.d) If in addition, lim k→∞ ∣∣∣∣σkνk ∣∣∣∣ = 0, then for every fixed T > 0, θ̂k,T → θ a.s. as k →∞and ∣∣∣∣νkσk ∣∣∣∣ (θ̂k,T − θ)→D ( T (α−1)/α2 )1/α S4 S3 as k →∞. Remark: The parabolicity condition and the MLE consistency condition in general are notconnected. Keywords: ada; anal; distribution; estimation; eur; https://doi.org/10.28924/ada/ma.3.4; i=1; levy; math; process; stochastic

## Model

- Analysis of a Mathematical Model Incorporating Dual Protection and ART Adherence for a High Risk HIV Population by Oriedo, I. S.; Lawi, G. O.; Bonyo, J. O. (2023) - The Zeros of the characteristic equation (14) Cases c0 c1 c2 c3 R0 > 1 Sign Change No. of - Roots1 + − − + R0 > 1 2 2,02 + − + + R0 > 1 2 2,03 − − + − R0 > 1 2 2,04 + + − − R0 > 1 1 05 − − + + R0 > 1 1 06 + + + − R0 > 1 1 07 − + − + R0 > 1 3 3,18 − − − − R0 > 1 0 0 This implies that for a small pertubation of the E1, solutions of the mathematical model representedby the system (2) always converge to E1, whenever R0 > 1. − αb1b6b8 − αb1b4b10 + b2b4b7Q2 + b1b5b8Q2 − b1b4b9Q2 − b1b4Q1Q2The number of negative zeros of equation (14) depends on the signs of c0, c1, c2 and c3. Keywords: hiv; model; risk; system; � �
- Modeling the Inflow of Exposed and Infected Migrants on the Dynamics of Malaria by Konlan, Musah (2024) - − − − 1 1 https://doi.org/10.28924/ada/ma.4.7 Eur. J. Math. Number (#) of Possible Positive Roots of f (I∗∗h ) Case q3 q2 q1 q0 # of sign change # of roots(i) + + + − 1 1(ii) + + − − 1 1(iii) + − + − 3 1, 3(iv) + Keywords: disease; equilibrium; malaria; math; model; rate
- Stability Analysis of a Mathematical Model for Examination Malpractice Dynamics by Konlan, Musah; Chuaya, Razak Gbemmie (2025) - Examination malpractice is one of the key challenges endangering the quality of educa-tion in Ghana. In this paper, we proposed a mathematical model for exploringthe dynamics of examination malpractice at the West African Senior School Certificate Examination(WASSCE) level in Ghana. Keywords: candidates; examination; malpractice; math; model
- Efficient Numerical Schemes for Computations of European Options with Transaction Costs by Hossan, Md. Shorif; Islam, Md. Shafiqul; Kamrujjaman, Md. (2022) - J. Monique, Y. Marc, C. March, Mathematical methods for financial markets, Springer Science & Business Media,2009.[4] J. R. Buchanan, An undergraduate introduction to financial mathematics, 3rd ed., World Scientific Publishing Com-pany, 2012.[5] A. Yves, P. Olivier, Computational methods for option pricing, Society for Industrial and Applied Mathematics, 2005.[6] J. Guyon, P. Henry-Labordere, Nonlinear option pricing, CRC Press, 2014.[7] F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Polit. nonlinear Black-Scholes PDE; option pricing; volatility model; finite volume method; finitedifference method. Keywords: black; equation; finite; math; model; option; pricing; scholes; volatility; σ̃ σ

## Lim

- The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces by Mendy, Sang B; Mendy, John T; Jobe, Alieu (2021) - + βn(ψ(q)− q) + αn(un − q), un+1 − q〉 ≤ (1− βn)2‖vn − q‖2 + 2βn‖ψ(xn)− ψ(q)‖‖un+1 − q‖+ 2αn‖un − q‖‖un+1 − q‖ +2βn〈ψ(q)− q, un+1 − q〉 ≤ (1− βn)2‖vn − q‖2 + 2βnα‖un − q‖‖un+1 − q‖+ 2αn‖un − q‖‖un+1 − q‖ +2βn〈ψ(q)− q, un+1 − q〉 ≤ (1− βn)2‖vn − q‖2 + (2βnα+ 2αn)‖un − q‖‖un+1 − q‖+ 2βn〈ψ(q)− q, un+1 − q〉 ≤ γ2ns 2 nk 2 n‖un − q‖2 + γ2n(1− sn)2k2n‖un+1 − q‖2 + [ γ2nsn(1− sn)k2n + 2(βnα+ αn) ] ‖un − q‖‖un+1 − q‖ +2βn〈ψ(q)− q, un+1 − q〉 (3.19) Eur. J. Math. Keywords: lim; q‖2
- Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces by Agwu, Imo Kalu; Igbokwe, Donatus Ikechi; Ukeje, Nathenial C. (2021) - − u‖ − ‖xn+1 − Sn,mu‖) = ψ−1(‖(xn − u‖ − ‖xn+1 − u + u − Sn,mu‖) ≤ ψ−1(‖(xn − u‖ − (‖xn+1 − u‖+ ‖Sn,mu − u‖)), (3.58) so that the sequence {bn.m} converges uniformly to 0, i.e, bn,m → 0 as n →∞. Since limn→Bn = 1and limn→∞ bn,m = 0, it follows from (3.57) that lim supn→∞ an(t) ≤ lim infb→∞ bn.m ≤ lim infn→∞ ν (1) n ≤ ‖Sn2xn − T2(PT2)n−1zn‖+ ‖yn − xn‖+Mhn(‖zn − xn‖) + Keywords: lim; n=1; q‖+; ‖xn
- Strong Continuity of Composition Semigroups on the Generalized Bloch Spaces of the Upper Half Plane by Wandera, K. A.; Bonyo, J. O.; Ambogo, D. O. (2023) - Therefore ‖Cϕt f − f ‖Bα(U) Therefore ‖Cϕt f − f ‖Bα(U) Keywords: bloch; bα0; lim
- Hybrid Inertial Iterative Method for Fixed point, Variational Inequality and Generalized Mixed Equilibrium Problems in Banach Space by Umar, Lawal; Ibrahim, Yusuf; Lawan, M.S. (2024) - We consider the following estimate using triangular inequality ‖xn − vn‖ ≤ ‖xn − xn+1‖+ ‖xn+1 Consider the triangular inequality ‖ ωn − zn ‖≤‖ ωn − xn ‖ + ‖ xn − zn ‖ . Keywords: i=1; lim; n→∞
- New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem by Ofem, Austine Efut; Udofia, Unwana Effiong; Igbokwe, Donatus Ikechi (2021) - − z‖ = x. (4.7) Again, using (1.7), we get ‖`s+1 − z‖ = ‖Tζs − z‖ ≤ ‖ζs − z‖ = ‖Tws − z‖ ≤ ‖ws − z‖ = ‖(1− δs)T`s + δsTgs − z‖ ≤ (1− δs)‖T`s − z‖+ δs‖Tgs − z‖ ≤ (1− δs)‖`s − z‖+ δs‖gs − z‖ = ‖`s − z‖ − δs‖`s − z‖+ δs‖gs − z‖. (4.8) From (4.8), we have ‖`s+1 − z‖ − ‖`s − z‖ δs ≤ ‖gs − z‖ − ‖`s − z‖. (4.9) − z‖ ≤ γ(1− δs)‖`s − z‖+ γδs(1− (1− γ)βs)‖`s − z‖ = γ(1− (1− γ)δsβs)‖`s − z‖. (3.2) From (1.7) and (3.2), we obtain ‖ζs − z‖ = ‖Tws − z‖ ≤ γ‖ws − z‖ ≤ γ2(1− (1− γ)δsβs)‖`s − z‖. (3.3) Using (1.7) and (3.3), we have ‖`s+1 − z‖ = ‖Tζs − z‖ ≤ γ‖ζs − z‖ ≤ γ3(1− (1− γ)δsβs)‖`s − z‖. (3.4) From (3.4), we have the following inequalities: ‖`s+1 − z‖ ≤ γ3(1− (1− γ)δsβs)‖`s − z‖ ≤ γ3(1− (1− γ)δs−1βs−1)‖`s−1 − z‖... ‖`1 Keywords: algorithm; iterative; lim; mappings; math; nonexpansive; − z‖

## Order

- Fractionalization of Hankel Type Integral Transforms and Their Relevance by Waphare, B. B.; Shaikh, R. Z. (2022) - In this paper, the fractionalization of certain types of Hankel transforms is suggested. Introduction The theory of Hankel transforms is very vast and it is studied by many researchers in recent aswell as in past. Keywords: hankel; operator; order; transform; type
- Finite Difference Method for Solving Second-Order Boundary Value Problems with High-Order Accuracy by Dung, Nguyen Dinh; Quang, Vu Vinh (2024) - − zi−1)(zi − zi+1)...(zi − zi−1)(x − zi+1)...(x Keywords: accuracy; boundary; grid; order; problem
- Analytical Approximations for the Principal Branch of the Lambert W Function by Howard, Roy M. (2022) - 1– e 1  W y  W2 W3 y WI3 y  re y  W0 y  W1 y  y W0 y  W2 y Keywords: approximations; error; figure; function; interval; lambert; lambert w; order; theorem; w y; wli; y y; y ; y ln;  w; ln+

## I=1

- On the Stratonovich Estimator for the Itô Diffusion by Bishwal, Jaya P. N. (2022) - 10.28924/ada/ma.2.7 2model was first studied by Dorogovcev (1976) who obtained weak consistency of the conditionalleast squares estimator (CLSE) under some regularity conditions as T →∞ and T n → 0. Kasonga(1988) and the resulting minimum contrast estimator, called the Euler estimator, is θ̌n,T := arg min θ∈Θ Hn,T (θ) Florens-Zmirou (1989) showed L2 consistency of the estimator as T →∞ and T n → 0.If continuous observation of {Xt} on the interval Keywords: i=1; xti−1
- Quasi-likelihood Estimation in Fractional Levy SPDEs from Poisson Sampling by Bishwal, Jaya P. N. (2022) - Continuoustime long memory jump process is fractional Levy process. Hence fractional Levy process can alsobe called the Kolmogorov-Levy process. Keywords: estimation; fractional; i=1; levy; process; stochastic
- Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps by Ravikumar, K.; Ramkumar, K.; Chalishajar, Dimplekumar (2021) - Similarly, for all t ∈ [tk, tk−1). x(t) = k∏ i=1 biC(t)u0 + k∏ i=1 biS(t)v0 + k∑ i=1 k∏ j=i bj ∫ ti ti−1 S(t − s)f(s)ds+ ∫ t ξk S(t − s)f(s)ds. − t0)∥∥∥∥φ − h(0, φ)∥∥ ]I[ξk ,ξk+1)(t)]2 Eur. J. Math. Keywords: i=1; max{1,n; s(t −; t t0; ξi−1

## Ada

- The Fractal Nature of Drought: Power Laws and Fractal Complexity of Arizona Drought by Azizi, Sepideh; Azizi, Tahmineh (2022) - In figure (7), we can see the fitted least squares approximation to the logarithm of powerspectral density of Arizona drought database. Moreover, we have plotted the scaling exponent graphs for Arizona drought database in figure (8). Keywords: ada; analysis; arizona; data; database; drought; figure; fractal; math; monitor; power; scaling; time

## Operator

- Duals of Continuous Frames in Hilbert C∗-Modules by Rossaf, Mohamed; Mabrouk, Khadija; Ghiati, M'hamed; Mouniane, Mohammed (2024) - Moreover, if B is an upper bound for {Fw}w∈Ω and S is frame operator of {Fw}w∈Ω, then B ∥∥S−1 ∥∥− 1 2 ‖TF‖−1 ‖Γ‖−1 is a lower bound for {gw}w∈Ω. Proof. Let F = {Fw}w∈Ω be a ∗-continuous frame for H with pre-frame operator TF and frame operator S. Then the set of all the operator duals of {Fw}w∈Ω is precisely the following {gw}w∈Ω = { ΓFw + ϕew − ∫ Ω 〈 S−1Fw , Fi 〉 ϕewdµ(ω) } w∈Ω , where {ew}w∈Ω is the standard orthonormal basis for L2(Ω,A), ϕ ∈ B∗ ( H, L2(Ω,A) ) , and Γ is an invertible adjointable operator on H. Proof. Keywords: frame; fw}w∈ω; operator
- ∗-K-Operator Frame for Hom∗A(X) by Rossafi, Mohamed; El Jazzar, Roumaissae; Kacha, Ali (2021) - Then by the uniqueness of frame operator, the last expression is equal to ST⊗P (ξ⊗η). = sup {p̄Y(T (x)) : ξ ∈ X , p̄X (ξ) 6 1}It’s clear to see that, p̂(T ) 6 ‖T‖∞ for all p ∈ S(A). Keywords: frame; operator

## Equation

- A Note on the Stability of Functional Equations via a Celebrated Direct Method by Zhang, Dongwen; Rassias, John Michael; Liu, Qi; Li, Yongjin (2022) - Furthermore, we continue to construct and study a couple of functional equations bymaking a new direct method. Introduction The core idea of the Hyers-Ulam stability for functional equations has been dated back to awell-known problem concerning about group homomorphisms solved by S.M. Ulam and D.H. Hyers(see Keywords: equation; math
- Group Analysis of Equal-Width Equation by Owino, Joseph Owuor (2023) - = τu = ξu 10.28924/ada/ma.3.13 13 dt 0 = dx 1 = du 0 , (3.46) yield two invariants, J1 = t and J2 = u. Keywords: equation; group
- Modulation Instability, Dark and Singular Soliton for Weakly Nonlocal Schrodinger Equation by Danladi, Ali; Tahir, Alhaji; Rezazadeh, Hadi (2025) - The study of Schrodinger equations with nonlinearity is an important area of research in math-ematical physics. The ability to obtain exact solutions to such complex equations is crucial in understandingthe underlying physics and designing new experiments. Keywords: equation; nonlinear; solutions; values; wave

## Theorem

- Slicing of Negative Plurisubharmonic Currents Arising From Analytic Subsets by Khedhiri, Hedi (2024) - × Cn−k , z = (z ′, z ′′), z ′ ∈ Ck , z ′′ ∈ Cn−k . Consider in C5 = C × C4, X = {z2 = z3 = z4 = 0} and Y = {z4 = z2 2 z 2 3} take k = 1 and ϕ(z ′) Keywords: theorem
- The Rellich-Kondrachov Theorem for Gelfand Pairs Over Hypergroups by Bataka, Ky T.; Mensah, Yaogan (2025) - 10.28924/ada/ma.5.3 3(2) ∀x, y ∈ H, supp(δx ∗ δy ) ⊂ H. Let G be a hypergroup and let K be a compact subhypergroup of G. For x, y ∈ G, x ∗ y standsfor the support of δx ∗ δy . the mapping (µ, ν) 7→ µ ∗ ν is continuous from Mb(G)×Mb(G) into Mb(G),(b) ∀x, y ∈ G, δx ∗ δy is a probability measure such that supp(δx ∗ δy ) is compact.(c) Keywords: theorem
- Nonlinear Geometry of Norm-Attaining Functionals: Variational Principles, Subdifferential Calculus, and Polynomial Optimization in Locally Convex Spaces by Evans, Mogoi N.; Moraa, Priscah (2025) - For any continuous quasilinear p : X → R, there exists f ∈ X∗ attaining its p-norm and separating A from B: sup a∈A f (a) ≤ inf b∈B f (b) Proof. B−K.By the nonlinear separation theorem (see [1]), there exists f ∈ X∗ with: sup k∈K f (k) ≤ inf b∈B f (b) Step 3: Norm-Attainment VerificationThe critical observation is that f attains its p-norm on ∂K: ∃x0 ∈ ∂K with f (x0) Keywords: attainment; convex; norm; theorem

## Fractional

- Conditional Least Squares Estimation for Fractional Super Levy Processes in Nonlinear SPDEs by Bishwal, Jaya P. N. (2024) - For a large class of Levy processes, MH is neither a semimartingale.3)MH is Hölder continuous of any order β less than H − 1 2 . 4) MH has stationary increments. 3) SH is Hölder continuous of any order β less than H − 1 2 . 4) Keywords: fractional; levy; math; process; processes; stochastic

## System

- Lie Group Analysis of a Nonlinear Coupled System of Korteweg-de Vries Equations by Owuor Owino, Joseph ; Okelo, Benard (2021) - One can easily see that if λ = − 12β α , and µ = 0, (72) then ϕ = − 12β αx2 , ψ = 0, (73) which is a solution of the system (61)-(62). Taking λ = − 6β α (75) gives µ = ± 6βi α , (76) with i2 = −1. Keywords: equations; group; lie; symmetry; system

## Norm

- On Norm Estimates for Derivations in Norm-Attainable Classes by Nyabonyi, J. Z.; Okelo, N. B.; Obogi, R. K. (2023) - https://doi.org/ 10.2307/2160991.[27] G. Lumer, Complex methods and the estimation of operator norms and spectra from real numerical ranges, J. Funct. derivation; norm; norm-attainability; Keywords: b(h; derivation; elementary; math; norm; operators; proof
- Computational Theory of Norm-Attaining Functionals: Algorithms, Stability, and Applications in Banach Spaces by Evans, Mogoi N.; Obogi, Robert (2025) - For regression models y = F (x) + ε with F ∈ X∗: (1) The empirical risk minimizer F̂n norm-attains with high probability (2) The attainment gap decays as E[‖F̂n‖ − sup‖x‖≤1 F̂n(x)|] Main Results and Discussions Theorem 2. Let X be a uniformly convex Banach space with modulus of convexity δ(ε), and let {Fn} be a sequence of computable functionals converging weakly to F ∈ X∗. Keywords: banach; computable; norm; space

## Graph

- On Degree-Based Topological Indices of Petersen Subdivision Graph by Ahmad, Mukhtar; Hussain, Saddam; Parveen, Ulfat; Zahid, Iqra; Sultan, Muhammad; Qayyum, Ather (2023) - index topological index of the general form, ⇒ SDD(G) Now putting the values in generalconnectivity index topological index of the general form, ⇒ M1(G) Keywords: graph; index; p(k; petersen; vertices
- Different Types of Topological Structures by Graphs by Asghar, Ali; Qayyum, Ather; Muhammad, Noor (2022) - Consider that G be simple graph, R = {((degG (u)u , degG (w)w )) ; u, w ∈ V }if l = 0 than R = {(lu)u , (mw )w , u, w ∈ W}if m = 1 and l = 0 than R = {(lu, lw ) u, w ∈ VConsider G is directed along with simple than R = {(lu, lw ) = (U,W ) u, w ∈ V } while if G is undirected than R = {(lu, lw ) Keywords: graph; k10

## Convex

- A Modified Algorithms for New Krasnoselskii's Type for Strongly Monotone and Lipschitz Mappings by Mendy, Furmose; Mendy, John T (2023) - − ρ∗‖2 − 2θnk‖xn − ρ∗‖2 + d2‖xn − ρ∗‖2 = ( θ2nL 2 − 2kθn + d2 ) ‖xn − ρ∗‖2 (3.4) Again, with the fact that 0 < ( θ2nL 2 − 2kθn + d2 ) Wm,p : Ju = ‖u‖2−pWm,p ∑ |α≤m| (−1)|α|Dα(|Dαu|p−2Dαu) ∈ W−m,p In Lp, `p and Wm,p spaces for 1 < p <∞ are q−uniformly smooth real Banach spaces with q, as q = min{2, p} and dq ≥ 1 (2.2) is given by dq = { 1+τq−1 (1+τ)q−1 , i f 1 < p < 2; p − 1, i f 2 ≤ p <∞. (2.3) and τ(0, 1) as the unique solution of the equation (q − 2)tq−1 + (q − 1)tq−2 − 1 = 0 It is well known that • E is smooth if and only if J is single-valued. • Keywords: convex; monotone
- Convexity Properties in Non-Newtonian Calculus and Their Applications by Wilbert, Asambo Awini; Iddrisu, Mohammed Muniru; Barnes, Benedict (2024) - The study presented some results on convexity properties in non-Newtonian calculus. Alsopresented is the Jensen-Steffensen inequality in non-Newtonian calculus and some applications. Keywords: convex

## Disease

- Local Stability Analysis of Onchocerciasis Transmission Dynamics With Nonlinear Incidence Functions in Two Interacting Populations by Adeyemo, K. M. (2023) - The following system of non-linear ordinary differential equations,with non-negative initial conditions, describes the dynamics of onchocerciaisis epidemics. dSh(t,xi ) Iv (t) − µh(xi)Sh + w(xi)Rh(t, xi)) dEh(t,xi ) dt = ∑L i=0 δλh(xi )Sh(t,xi ) Keywords: disease; i=0; µh(xi

## Frame

- Frame Operators for Frames in Krein Spaces by Jahan, Shah; Johnson, P. Sam (2024) - Krein space; Bessel sequence; frame sequence; frame operator.1 https://adac.ee https://doi.org/10.28924/ada/ma.4.1 https://orcid.org/0000-0002-5966-9185 https://orcid.org/0000-0003-3461-5380 Eur. Motivated by the equivalentdefinition of frame as given in (1), in this paper, we propose an alternative way of looking at thenotion of frames in Krein spaces by decomposing the index set I in a natural way and obtain somenew results on frames sequences. Keywords: frame; krein; space

## Scheme

- Numerical Stabilities of Vasicek and Geometric Brownian Motion Models by Badibi, O. C.; Ramadhani, I.; Ndondo, M. A.; Kumwimba, S. D. (2023) - In this article we establish and prove the conditions of numerical schemes stabilities in Mean andMean-square. Stochastic numerical schemes. Keywords: euler; maruyama; mean; scheme; θ1∆t; θ2∆t

## I=0

- Global Stability Analysis of Onchocerciasis Transmission Dynamics with Vigilant Compartment in Two Interacting Populations by Adeyemo, K. M. (2024) - 10.28924/ada/ma.4.9 2The case of onchocerciasis model presented in this paper incorporates a new class of humancompartment called vigilant individuals denoted by Vh(t, xi). + ( Ev − E∗∗v − E∗∗v ln Ev E∗∗v ) + αv + µv αv [ Iv − I∗∗v − I∗∗v ln Iv I∗∗v ] With Lyapunov time-derivative given as Ṁ = Ṡh(t, xi)− S∗∗h (xi) Sh(xi) Ṡh(t, xi) + Ėh(t, xi)− E∗∗h (xi) Eh(xi) Ėh(t, xi) + L∑ i=0 αh(xi) + µh(xi) αh(xi) ( İh(t, xi)− I∗∗h (xi) Ih(xi) İh(t, xi) ) + Ṡv − S∗∗v Sv Ṡv + Ėv − E∗∗v Ev Ėv + αv + µv αm ( İv − I∗∗v Iv İv ) (3.2) https://doi.org/10.28924/ada/ma.4.9 Eur. J. Math. Keywords: i=0

## Data

- A Proposal of New Extended Symmetric Cosine Distribution by Chesneau, Christophe (2025) - We start this analysis with the mean and variance associated withthe ESC distribution in the result below. We present them below, considering a random variable X withthe ESC distribution. Keywords: data; distribution; esc; esc distribution; math; pdf

## Inequality

- Coordination of Classical and Dynamic Inequalities Complying on Time Scales by Sahir, Muhammad Jibril Shahab (2023) - We explore dynamic inequalities on delta calcu-lus and their symmetric nabla versions. Thishybrid theory is also widely applied on dynamic inequalities. Keywords: inequality

## I∈[m

- Woven K-g-Fusion Frames in Hilbert C∗-Modules by Nhari, Fakhr-dine; Rossafi, Mohamed (2023) - Assume that f ∈ H and {σi}i∈[m] ∈ J, so ∑ i∈[m] ∑ j∈σi v2 i j 〈Λi jPW̃i j f ,Λi jPW̃i j f 〉 = ∑ i∈[m] ∑ j∈σi v2 i j ∑ k∈Ii j 〈Λi jPW̃i j f , f (k) i j 〈Λi jPWi j fn,Λi jPWi j fn〉 < 1 n 〈K∗fn, K∗f1〉, where, Kn = ∪i≥kn+1Jj . Keywords: i∈[m; j f; jpwi j; λi j

## Θ̃t

- On the Kolmogorov Distance for the Least Squares Estimator in the Fractional Ornstein-Uhlenbeck Process by Bishwal, Jaya P. N. (2023) - IT − 2H ( T −σ2H θ̃T )1/2 σ2Hb0θx ⇒ 2H ( T −σ2H θ̃T )1/2 (θ̃T − θ)[IT − b0T (θT − θ)] > x IT − 2H ( T −σ2H θ̃T )1/2 2b0θx  ⇒ (θ̃T − θ)IT − b0T (θ̃T − θ)2 > ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 ⇒ −NT + (θ̃T − θ)IT − b0T (θT − θ)2 > −NT + ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 ⇒ 0 > −NT + ( −σ2Hθ 4TH2 )1/2 IT x − σ2Hb0θx2 since IT − b0T (θ̃T − θ) > Tc0 − b0T (θ̃T − θ) > 2σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 − σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 = σ2Hb0(logT )1/2 ( −σ2Hθ 4TH2 )1/2 > 0. [IT − ( T −σ2H θ̃T )1/2 σ2Hb0θx ] ⇒ (θ̂T − θ)IT − b0T (θ̂T − θ)2 > ( T −σ2H θ̃T )−1/2 IT x − σ2Hb0θx2 ⇒ −MT + (θ̂T − θ)IT − b0T (θ̂T − θ)2 > −MT + ( T −σ2H θ̃T )−1/2 IT x − σ2Hb0θx2 ⇒ 0 > −MT + ( −σ2H θ̃T T )1/2 IT x − σ2Hb0θx2 since IT − b0T (θ̂T − θ) > Tc0 − b0T (θ̂T − θ) > 2σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 − σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 = σ2Hb0(logT )1/2 ( −σ2H θ̃T T )1/2 > 0. Keywords: t −σ2h; θ̃t; − θ; −σ2h θ̃t

## Eθt

- On the Kolmogorov Distance for the Maximum Likelihood Estimator in the Explosive Ornstein-Uhlenbeck Process by Bishwal, Jaya P. N. (2023) - 10.28924/ada/ma.3.25 4 i.e., e−2θT IT D→ ξ2 2θ as T →∞.It can be shown that e−2θT IT → ξ2 2θ almost surely as T →∞. (1.18)By Itô formula, we have ZT = ∫ T 0 XsdWs = ∫ T 0 eθsξsdWs = ∫ T 0 ξsdηs = ξTηT − T − ∫ T 0 ηsdξs = ξTηT − T − ∫ T 0 ηse −θsdWs . − ξ)2 → 0 as T →∞, (2.21) E(ξt − ξs)2 ≤ C(t − s). Keywords: eθt; e−2θt; θt −

## L1ω(g

- On a Generalization of (Lω1, Lωp)-Multipliers by Tissinam, Yaovi A.; Issa, Abudulaï; Mensah, Yaogan (2023) - We denote by L1ω(G) this new Banach algebra ; in other words L1ω(G) = (L1ω(G), ‖ · ‖1,ω, ∗ω).For s ∈ G, define the operator Γsω by Γsωf (x) = τsMωf (x) ω(x) , f ∈ L1ω(G), where Mω is the multiplication operator defined by (Mωf )(x) = ω(x)f (x) and τs is the translation operator defined by (τs f )(x) = f (s−1x). Also, define µ ∗ω f (x) = ∫ G f (y−1x) ω(y)ω(y−1x) ω(x) dµ(y) for f ∈ L1ω(G) and µ ∈ M1ω(G). Keywords: l1ω(g; multipliers

## Y‖2

- The Constants to Measure the Differences Between Isosceles and α-β Orthogonalities by Ni, Qichuan; Liu, Qi; Zhou, Yin; Qian, Qin (2024) - We get ‖αx − βy‖ = 2β, ‖x − y‖ = ‖x − βy‖ = ‖αx − y‖ = 2. We get ‖αx − βy‖ = β, ‖x − y‖ = ‖x − βy‖ = ‖αx − y‖ = 1. Keywords: y‖2

## 2πi

- On the Dirichlet Boundary Value Problem for the Cauchy-Riemann Equations in the Half Disc by Darya, Ali; Tagizadeh, Nasir (2024) - = 1 2πi ∫ ∂M ω(t) dt t − z − 1 π ∫ M ωt̄(t) dξdη t − z . Many results have been obtained for boundary value problems of complex partial differentialequations in some particular domains, see, e.g. [1–16]. Keywords: 2πi

## B∞,

- Duality of the Nonreflexive Bergman Space of the Upper Half Plane and Composition Groups by Gori, E. O.; Bonyo, J. O. (2024) - Now, g = f ◦ ψ is continuous on D with f = g ◦ ψ−1, and sup z∈D\ψ−1(K) 10.28924/ada/ma.4.14 10Now, lim a→0 ‖Cha f − f ‖B∞,◦(D) = lim a→0 ( sup z∈D (1− |z |2)|(Cha f − f )′|(z) ) Keywords: b∞,

## Inequalities

- Tensorial Simpson 1/8 Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space by Stojiljković, Vuk; Dragomir, Sever Silvestru (2024) - Reflected in this work is the tensorial Shuang’s Lemma, which asa consequence enabled us to obtain Simpson type inequalities in Hilbert space. The first paper related to tensorial inequalities in Hilbert space was written by Dragomir [13].In the paper, he proved the tensorial version of the Ostrowski type inequality given by the following. Keywords: inequalities; math

## Curve

- The Jacobi Mate of an Oval by Crasmareanu, Mircea (2024) - Jacobi elliptic functions; oval; support function; curvature.1 https://adac.ee https://doi.org/10.28924/ada/ma.4.18 https://orcid.org/0000-0002-5230-2751 Eur. J. Math. Recall that its solutions are called Jacobi elliptic functions and there are usually denoted cn(·, ρ), sn(·, ρ) respectively dn(·, ρ); we prefer the simple notation used above. Keywords: curve

## A∗η

- On η-Local Functions in Ideal Topological Spaces by Almocera, Junvon A.; Tutanes, Lezel M. (2025) - Now, notethat A∗η = η-cl(A∗η) and by Theorem 1 (x), hence, A∗η = η-cl(A∗η) ⊆ η-cl(A). For U ∈ η-O(X), suppose that x ∈ U ∩A∗η . Keywords: a∗η

## Logq

- Some Properties on The [p,q]-Order of Meromorphic Solutions of Homogeneous and Non-homogeneous Linear Differential Equations With Meromorphic Coefficients by Saidani, Mansouria; Belaidi, Benharrat (2021) - First, we will prove that f must be a polynomialwith deg f ≤ s − 1. = µp (f ) is the iterated lower p-order, λ[p,1] (f − a) = λp (f , a)(or λ[p,1] (f − a) = λp (f , a)) is the iterated convergence exponent of the sequence of distinct a-points (or of a-points), λ[p,1] (1f ) = λp ( 1 f ) is the iterated exponent of convergence of the poles, see [7] , [11] , Keywords: logq; ρ[p

## Lp)α

- Boundedness of Some Commutators in Total Fofana Spaces by Nagacy, Pokou (2024) - In this paper, we find necessary and sufficient conditions for the boundedness of the com-mutator of the Hardy-Littlewood maximal operator in total Fofana spaces. Total Fofana spaces; maximal operator; commutator; sublinear operators; BMO spaces.1 https://adac.ee https://doi.org/10.28924/ada/ma.4.22 Eur. J. Math. Keywords: lp)α; λ(rd

## S(z

- Correspondences Among Inner Functions, Functions with Non-Negative Real Parts and Conformal Mappings by Peretz, Ronen (2025) - Namely, ∀ z ∈ U , the function of w ∈ U given by: exp (−G(z · w)) is a contraction and so by the theoremof Banach it has a unique fixed-point w = S(z). The function of t ∈ U given by exp (−F (z · t)) is a contraction (with respect to the Euclideanmetric) where z ∈ U is fixed.(iv) Keywords: s(z

## Liouville

- Extremal Functions and Calderon’s Formulas for the Riemann-Liouville Two-Wavelet Transform by Chana, Ahmed; Akhlidj, Abdellatif (2024) - Let s > 2α+3 2 , ψ be aRiemann-Liouville wavelet on K in L2α(K) and β > 0 thenwe have f ∈ Hsψ,β(K)⇒ Fα(f ) Let f ∈ Hsψ,β(K), by using the relations (2.9), (3.9), (4.2) and (4.4) we find that ‖f Keywords: liouville; riemann

## Solution

- Stability of Positive Weak Solution for Generalized Weighted p-Fisher-Kolmogoroff Nonlinear Stationary-State Problem by Khafagy, Salah A.; Serag, Hassan M. (2022) - In the present paper, we investigate the stability results of positive weak solution for thegeneralized Fisher–Kolmogoroff nonlinear stationary-state problem involving weighted p-Laplacianoperator −d∆P,pu = ka(x)u[ν − υu] in Ω, Bu = 0 on ∂Ω, where ∆P,p with p > 1 and P = P (x)is a weight function, denotes the weighted p-Laplacian defined by ∆P,pu ≡ div In this paper we study the stability results of positive weak solution for the generalized weighted p-Fisher–Kolmogoroff nonlinear stationary-state problem −d∆P,pu = ka(x)f (u) = ka(x)u[ν − υu] in Ω, Bu = 0 on ∂Ω, } (1.1) where ∆P,p with p > 1 and P = P (x) is a weight function, denotes the weighted p-Laplaciandefined by ∆P,pu ≡ div [P (x)|∇u|p−2∇u] (see for details [6]), the continuous function a(x) : Keywords: solution

## K=1

- Some New Series Expansions of a Special Type of Functions Involving the Logarithmic Function by Chesneau, Christophe (2025) - − 1)− 2k−1(x2−k − 1) ] cos [ 2k−2(x2 −(k−1) − 1)− 2k−1(x2−k − 1) ] cosh Keywords: k=1; log(x; −k −

## Sequences

- Majorizing Sequences for Newton-Like Method and Their Limit Points by Argyros, Ioannis K.; George, Santhosh; Argyros, Michael (2025) - − xn‖ ≤ v∗ − vn. − xn‖ ≤ s∗ − sn. Keywords: sequences

## R+q

- Uncertainty Principles and Extremal Functions for Bessel Multiplier Operators in Quantum Calculus by Chana, Ahmed; Akhlidj, Abdellatif (2025) - Let f ∈ L2α(R+q ) and σ ∈ L2α(R+q ) ∩ L∞α (R+q ) satisfy the admissibility condition (3.7) and 0 < γ < δ <∞. Then the function fγ,δ(x) [12] (i) Let E be a measurable subset of R+q , we say that the function f ∈ L2α(R+q ) is ε-concentrated on E if ‖f − 1Ef ‖2,q,α ≤ ε‖f ‖2,q,α, (3.11) where 1E is the indicator function of the set E. (ii) Let F be a measurable subset of R+q × R+q , we say that the function Tσ,β(f ) is ρ-concentrated on F Keywords: r+q

## Dνα

- On a Family of q-Weighted Bergman Spaces and Applications by Nemri, Akram (2025) - [∇α,q, Lα,q]q := ∇α,qLα,q − Lα,q∇α,q = q−α−1Λq ( [α+ 1]qI + (1 + q−1)q−α−1Nq ) , where I is the identity operator and Λq is the q-shift operator given by Λqf (z) = f (qz). = Aα,q ⊕A⊥α,q then for any f ∈ L2α,q(D), we have f = (f − f ⊥) + f ⊥ where f − f ⊥ ∈ Aα,q and f ⊥ ∈ A⊥α,q . Keywords: dνα; q(d; q(z

## Variable

- Estimates of Variable Kernel Parameterized Littlewood-Paley Operators on Variable Herz Spaces by Abdalmonem, Afif; Khalil, Omer; Abdalrhman, Omer (2025) - j.aml.2011.11.022[18] A. Abdalmonem, O. Abdalrhman, S. Tao, Boundedness of fractional integral with variable kernel and their commuta-tors on variable exponent Herz spaces, Appl. [4].As is well known, over the past thirty years, variable kernel integral operators have become anincreasingly active area of research. Keywords: variable; µ∗,σψ

## Γ(α2

- Nonlinear Differential Problem with p-Laplacian and via Phi-Hilfer Approach: Solvability and Stability Analysis by Beddani, Hamid; Beddani, Moustafa; Dahmani, Zoubir (2021) - Prime value problems involving fractional Hilfer derivatives have been studiedby several authors, see [9,10,26]. https://doi.org/10.1016/j.camwa.2012.01.009.[10] H. Gu and J. J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Keywords: γ(α2; ϕγ2−1

## J(ρ

- Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings by Agwu, Imo Kalu; Igbokwe, Donatus Ikechi (2021) - × ( α `s−1 n,1 + `s∑ j=2 α `s−1 n,j j−1∏ i=1 (1− α`s−1n,i ) + `s∏ i=1 (1− α`s−1n,i ) ) Putting (4.8) in (4.7), we obtain, using Lemma 2.3 that the sequence {tn}∞n=0 converges strongly tothe point q in F (Γ).On the other hand, suppose tn → q as n → ∞. Then, we show that ε → 0 as n → ∞. Indeed,from (3.5) with v1n = y1n , (4.2) and Proposition 2.4 with u = q, v1n = t, j = i , k = 1,Γj−1v1n = vj−1and Γ`1v1n = v „ we have εn = ‖tn+1 − δn,1v1n,1 − `1∑ j=2 δn,j j−1∏ i=1 (1− δn,i)Γj−1v1n − `1∏ i=1 (1− δn,i)Γ`1v1n ‖2 = ‖tn+1 − q − δn,1v1n,1 + `1∑ j=2 δn,j j−1∏ i=1 (1− δn,i)Γj−1v1n + `1∏ i=1 (1− δn,i)Γ`1v1n − q  ‖2 ≤ ‖tn+1 − q‖2 + ‖δn,1v1n,1 + `1∑ j=2 δn,j j−1∏ i=1 (1− δn,i)Γj−1v1n + `1∏ i=1 (1− δn,i)Γ`1v1n − q‖2 ≤ ‖tn+1 − q‖2 + δn,1‖v1n,1 − q‖2 + `1∑ j=2 δn,j j−1∏ i=1 (1− δn,i)‖Γj−1v1n − Γj−1q‖2 + `1∏ i=1 (1− δn,i)‖Γ`1v1n − Γ`1q‖2 ≤ ‖tn+1 − q‖2 + δn,1‖v1n,1 − q‖2 + `1∑ j=2 δn,j j−1∏ i=1 (1− δn,i)(ρj)2‖v1n − q‖2 + `1∏ i=1 (1− δn,i)(ρj)2‖v1n − q‖2 https://doi.org/10.28924/ada/ma.2.1 Eur. − q‖2 ≤ δn,1‖xn − q‖2 + `1∑ j=2 δn,j(ρ j)2 j−1∏ i=1 (1− δn,i)‖y1n − q‖2 + `1∏ i=1 (1− δn,i)(ρj)2‖y1n − q‖2 = δn,1‖xn − q‖2 + ( 1− δ1n,1 − `1∏ i=1 (1− δn,i)(ρj)2 ) ‖y1n − q‖2 + `1∏ i=1 (1− δn,i)(ρj)2‖y1n − q‖2 = δn,1‖xn − q‖2 + ( 1− δ1n,1 ) ‖y1n − q‖2 (3.6) Since `1, `k are fixed integers and αsn,i ∈ Keywords: j j−1∏; j(ρ; j=2; j=2 α1n; j=2 δn; j−1∏ i=1; α1n; α2n; α3n; − q‖2

## Αq‖2

- Weak and Strong Convergence Theorems of Modified Projection-Type Ishikawa Iteration Scheme for Lipschitz α-Hemicontractive Mappings by Agwu, lmo; Igbokwe, Donatus Ikechi (2022) - δn)(1− γn)‖xn − αq‖2 + γnL 2‖yn − αq‖2 − δnγnL2‖yn − αq‖2 −(γn − δnγn − γ2n)[(1 + L)‖xn − αq‖2 + L(1 + L)‖yn − αq‖2]− δn(1− δn)‖xn − αq‖2 = (1− − αq‖2 − ‖xn − αq‖2 + (1− γn − γnL)β2nγnL‖xn − Txn‖2 ≤ δnB. (3.22) Keywords: math; αq‖2

## 0(ω

- Unilateral Problem for a Viscoelastic Beam Equation Type p-Laplacian with Strong Damping and Logarithmic Source by Pereira, Ducival C.; Araújo, Geraldo M. de; Raposo, Carlos A. (2022) - In [3] the authors establish existence of global solution to the problem utt + ∆2u − ∆pu + ∫ t 0 g(t − s)∆u(s)ds − ∆ut + f (u) = 0 in Ω× R+, (1.1) [12]The problem (1.1), with its memory term ∫ t 0 g(t− s)∆u(s)ds , can be regarded as a fourth-orderviscoelastic plate equation with a lower order perturbation of the p-Laplacian type. Keywords: 0(ω; l2(0; math

## C∗-algebra

- On the α−ψ−Contractive Mappings in C∗-Algebra Valued b-Rectangular Metric Spaces and Fixed Point Theorems by Rossafi, Mohamed; Kari, Abdelkarim; Massit, Hafida (2022) - � y if and only if y − x � θwhere θ means the zero element in A. we denote the set x ∈ A : x This is clear that T is α− ψ− contractive mapping and satisfies α(x, y)d(Tx, T y) � ψ(d(x, y)), for all x, y ∈ X Theorem 3.4. Keywords: c∗-algebra

## Orthogonality

- A New Approximate Birkhoff Orthogonality Type by Zhou, Chuanjiang; Liu, Qi; Li, Yongjin (2022) - y‖ − ‖ax‖ − (‖x − ax − y‖+ ‖ax‖) ≤ ‖x + ax + y − ax‖ − ‖x − ax − y + ax‖, and ‖x + ax + y − ax‖ − ‖x − ax − y + ax‖ ≤ ‖x + ax + y‖+ ‖ax‖ − (‖x − ax − y‖ − ‖ax‖). y‖ = ‖x − ax − y‖, then |‖x + y‖ − ‖x − y‖| = |‖x + ax + y − ax‖ − ‖x − ax − y + ax‖|. Keywords: orthogonality; spaces

## Epilogue

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Created: 2025-12-23