Suzuki-Edelstein Type Contractions via Auxiliary Functions

Abstract

We prove the existence and uniqueness of a fixed point of certain type mapping, extension of Suzuki-Edelstein mapping, in a partially ordered complete metric space. Our results extend, improve, and generalize the existence results on the topic in the literature. We state some examples to illustrate our results.

Various Suzuki type theorems in b -metric spaces

“…In 2009, Suzuki [27] proved certain remarkable results to improve the results of Banach and Edelstein (see also [24,26]). Now, we are ready to prove the following Suzuki type theorems for nonlinear contractions.…”

Discussions on Recent Results forα-ψ-Contractive Mappings

“…Recently Miandaragh et al [13] proved certain results for generalized convex contractions on complete metric spaces. Salimi et al [14] modified the concept ofadmissible mappings introduced and studied by Samet et al [15], Karapınar and Samet [16], and Salimi and Karapınar [17]. We establish certain fixed point results for --generalized convex contractions, --weakly Zamfirescu mappings, and --Ćirić strong almost contractions.…”

Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

“…In consistence with [33], we denote Φ ϕ the set of functions ϕ : [0, ∞) → [0, ∞) satisfying the following condition:…”

“…Salimi et al [33] prove the existence and uniqueness of a fixed point results of Suzuki-Edelstein mapping, in a partially ordered complete metric space. In 2005, Eldred et al [21] gave existence and convergence of best proximity points in the setting of a uniformly convex Banach space.…”