Coupled fixed point theorems for rational type contractions

Abstract

In this paper, we will consider the coupled fixed problem in $b$-metric space for single-valued operators satisfying a generalized contraction condition of rational type. First part of the paper concerns with some fixed point theorems, while the second part presents a study of the solution set of the coupled fixed point problem.
More precisely, we will present some existence and uniqueness theorems for the coupled fixed point problem, as well as a qualitative study of it (data dependence of the coupled fixed point set, well-posedness, Ulam-Hyers stability and the limit shadowing property of the coupled fixed point problem) under some rational type contraction assumptions on the mapping.