Introducing Monotone Enriched Nonexpansive Mappings for Fixed Point Approximation in Ordered CAT(0) Spaces

The aim of this paper is twofold: introducing the concept of monotone enriched nonexpansive mappings and a faster iterative process. Our examples illustrate the novelty of our newly introduced concepts. We investigate the iterative estimation of fixed points for such mappings for the first time within an ordered CAT(0) space. It is done by proving some strong and Δ-convergence theorems. Additionally, numerical experiments are included to demonstrate the validity of our theoretical results and to establish the superiority of convergence behavior of our iterative process. As an application, we use our newly introduced concepts to find the solution of an integral equation. The outcomes of our study expand upon and enhance certain established findings in the current body of literature.