New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov process

Abstract

In this paper, we define a generalized $T$-contraction and derive some new coupled fixed point theorems in cone metric spaces with total ordering condition. An illustrative example is provided to support our results. As an application, we utilize the results obtained to study the existence of common solution to a system of integral equations. We also present an application to Markov process.