Perturbed Graphical Metric Spaces and Fixed Point Theory

Taking into account the recent view of fixed point theory as expressed by Jalali and Samet [On Banach's fixed point theorem in perturbed metric spaces, J. Appl. Anal. Comput.  ۱۴ (۲) (۲۰۲۵), ۹۹۲--۱۰۰۱], we first introduce a perturbed metric space equipped with a graph and then present new concepts and notions related to this space. Next, we prove some fixed point theorems related to this new space. Several consequences and an example are also presented to demonstrate the effectiveness of the main results. Following the idea of this article, one can continue this new way to obtain fixed points of the mappings that do not satisfy classic contractions in such spaces endowed with a graph or a partial order.

Keywords:

Perturbed graphical metric space , Orbitally \mathcal{H}-continuous , Perturbed \mathcal{H}-quasi-contractions , Fixed point