id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-7124	Kumar, Manoj; Bhardwaj, Neha; Mani, Gunaseelan; Ramaswamy, Rajagopalan ; Hayat Khan, Khizar; Abdelnaby, Ola Ashour A	Fixed Point Theorems for (β, φ)-Expansive Mappings in Controlled Metric Space	2025	14	.pdf	application/pdf	4617	325	86	Let Ω = [0,∞) with controlled metric space d̄ : Ω × Ω → [0,∞) defined by d̄ = |u − e| ∀ u, e ∈ Ω along with the mapping µ : Ω × Ω → [1,∞) and define T : Ω → Ω is (β, φ)-expansive mapping with φ ∈ Φ by T (u) = { u3, u ≥ 1 2 , u 2 , 0 ≤ u < 1 2 and β(u, e) = { 0, u, e ≥ Let Ω be a non-empty set and µ : Ω × Ω → [1,∞) be a mapping.	cache/ejpam-7124.pdf	txt/ejpam-7124.txt