On the existence of coincidence and common fixed point of two rational type contractions and an application in dynamical programming

TL;DR

This paper proves new coincidence point theorems for rational contractions in generalized metric spaces, extending existing results and applying them to solve functional equations in dynamic programming.

Contribution

It introduces novel coincidence point results for rational contractions in generalized metric spaces, broadening the scope of fixed point theory and its applications.

Findings

Established new coincidence point theorems for rational contractions

Extended and generalized existing fixed point results

Applied theorems to solve functional equations in dynamic programming

Abstract

In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results applies, in particular, to the study of solvability of functional equations arising in dynamic programming.