# Tripartite coincidence-best proximity points in generalized metric spaces

## TL;DR

This paper introduces a new framework for analyzing tripartite coincidence and best proximity points in generalized metric spaces, establishing existence and convergence theorems for these points.

## Contribution

It develops a novel notion of convex structure and tripartite contractions in generalized metric spaces, expanding fixed point theory to more complex mappings.

## Key findings

- Existence of tripartite coincidence points
- Convergence of iterative sequences to best proximity points
- Extension of fixed point results to generalized metric spaces

## Abstract

We first introduce a notion of convex structure in generalized metric spaces, then we introduce tripartite contractions, tripartite semi-contractions, tripartite coincidence points, as well as tripartite best proximity points for a given triple $(K;S;T)$ of nonlinear mappings defined on the union $A\cup B\cup C$ of closed subsets of a generalized metric space. We prove theorems on the existence and convergence of tripartite coincidence-best proximity points.