Fixed point theorems for generalized α−η−ψ− Geraghty contraction type mappings in α−η− complete metric spaces

Abstract

In this paper, we introduce the concept of generalized α-η-ψ-Geraghty contraction type mappings and prove the unique fixed point theorems for such mappings in α-η-complete metric spaces without assuming the subadditivity of ψ. We also give an example for supporting the result and present an application using our main result to obtain a solution of the integral equation.

C -class functions and fixed point theorems for generalized α−η−ψ−φ−F− contraction type mappings in α−η− complete metric spaces

“…The following ordinary differential equation is taken from Karapinar [11] and Chaudchawna et al [6] :…”

Best proximity points for generalized - α - η- ψ - Geraghty proximal contraction mappings

“…As an application of our results, we prove this fixed point theorem which is proved by Chuadchawna et al [6] as follows.…”

“…Theorem 1.1. [6] Let (X, d) be a metric space. Assume that α, η : X ×X → [0, ∞) be functions and T : X → X be mapping .…”

Maia type fixed point results via C-class function

“…Lemma 2 [9] Suppose (X, δ) be a metric space. Let {x n } be a sequence in X such that δ(x n , x n+1 ) → 0 as n → ∞.…”