Investigating a Common Fixed Point for Two Mappings in F-Modular-B-Metric Space: Application in Graph Theory"

Resumen

Here, a new framework for common fixed point (CFP) of a family of two mappings
in the setting of F-modular b-metric spaces (FMbMS) will be used to investigate
the relation of fixed points in graph theory. As a novel interplay between metric
and graph-like structures, this discovery integrates and generalizes many of those
in both graph and fixed-point theories.We provide graphical representations and
examples showing how our ideas can be applied to solve dynamics, network analysis,
and optimization problems. In addition to bridging the gap between graph
theory and fixed point theory, our work opens up new research directions in the
study of complex systems and the underlying structures of those systems.