A fixed point theorem in generalized ordered metric spaces with application

Abstract

In this paper, we consider the concept of Ω-distance on a complete, partially ordered G-metric space and prove a fixed point theorem for (ψ, φ)-Weak contraction. Then, we present some applications in integral equations.

Existence of unique common solution to the system of non-linear integral equations via fixed point results in incomplete metric spaces

“…Many mathematicians applied fixed point methods to the existence of unique solutions to non-linear integral equations, for example, refer to [3, 4, 9, 13–16]. Particularly, Sintunavarat et al [4] and Rashwan and Saleh [17] established fixed point results to find the existence of a unique common solution to a system of Urysohn integral equations.…”

Coupled coincidence point results in partially ordered generalized fuzzy metric spaces with applications to integral equations

“…The generalization is effectuated by a non-negative real-valued mapping on X 3 ; where X is a given non-empty set on which the generalized metric is defined. Fixed point results on this structure were proved in a good number of papers, as, for instance [1,5,8,10,19].…”

A coincident point principle for two weakly compatible mappings in partial S-metric spaces

“…For example, see [1,2,3,4,5,6,8,11,13,15,17,18,19,20,21]. However, many researchers prove the existence and uniqueness of a coincident point and common fixed point for two self-mappings on different types of metric spaces.…”