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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
