On common fixed point for finite family on maps in a relational metric space

Abstract

This research establishes new coincidence and common fixed-point theorems for finite families of self-mappings in complete metric spaces endowed with binary relation. Extending the relational framework initiated by Samet and Turinici and later developed by Shatanawi and Sintunavarat, we introduced g-comparative mappings and prove existence and uniqueness theorems for coincidence and common fixed points of families and single map g. The main results are obtained under a generalized contractive inequality where  is comparison function and is auxiliary metric expression. By assuming relational regularity, weak compatibility, and the existence of an admissible initial point, we construct a modular-iterative sequence and prove its convergence to unique common fixed point. A numerical example is given to describe how the scheme works.