Fixed point results in R-enriched interpolative Kannan pair in R-Convex metric spaces

TL;DR

This paper introduces R-enriched interpolative Kannan pairs in R-convex metric spaces, establishing fixed point theorems and analyzing stability properties, thereby extending existing fixed point results in metric space theory.

Contribution

It presents a new class of fixed point mappings in R-convex metric spaces and proves a common fixed point theorem, extending prior results in the literature.

Findings

Established a common fixed point theorem for R-enriched interpolative Kannan pairs.

Demonstrated the well-posedness and Ulam-Hyers stability of the mappings.

Provided examples supporting the theoretical concepts.

Abstract

The purpose of this paper is to introduce the class of R-enriched interpolative Kannan pair and proved a common fixed point result in the context of R-complete convex metric spaces. Some examples are presented to support the concepts introduced herein. Moreover, we study the well-posedness, limit shadowing property and Ulam-Hyers stability of the mappings introduced herein. Our result extend and generalize several comparable results in the existing literature.