Abstract
We introduce the concept of a -compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with -distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend, and unify several well-known comparable results in the literature.
Highlights
Introduction and PreliminariesIn 1996, Kada et al 1 introduced the notion of w-distance
They elaborated, with the help of examples, that the concept of w-distance is general than that of metric on a nonempty set. They proved a generalization of Caristi fixed point theorem employing the definition of w-distance on a complete metric space
Ilicand Rakocevic 2 obtained fixed point and common fixed point theorems in terms of w-distance on complete metric spaces see 3–9
Summary
In 1996, Kada et al 1 introduced the notion of w-distance. They elaborated, with the help of examples, that the concept of w-distance is general than that of metric on a nonempty set. Bhaskar and Lakshmikantham in introduced the concept of coupled fixed point of a mapping F : X ×X → X and investigated some coupled fixed point theorems in partially ordered sets. They discussed an application of their result by investigating the existence and uniqueness of solution for a periodic boundary value problem. Lakshmikantham and Ciric proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces which extend the coupled fixed point theorem given in 11. We will consider that x, y and u, v are comparable with respect to ordering in X × X if x u and y v
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