Uniqueness of Stationary Distribution in Markov Processes: A Quintuple Fixed Point and Coincidence Point Approach

This article introduces the concept of quintuple fixed points and coincidence points for matrix-related mappings in generalized metric spaces. Furthermore, the existence of quintuple coincidence points is established. This task is achieved by leveraging the structure of matrices. We derive several corollaries as special cases of our main results. These corollaries provide evidence for the authentication of the proven results. To validate the significance of our findings, we provide a selection of non-trivial examples. Eventually, we demonstrate the practical applicability of our established results by applying them to determine the stationary distribution of a Markov process.