id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ma-50	Agwu, Imo Kalu; Igbokwe, Donatus Ikechi	Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings	2021	38	.pdf	application/pdf	12927	440	82	× ( 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 ∈	cache/ma-50.pdf	txt/ma-50.txt
