An Analysis on Some New Fixed Point Theorem in Generalized Modular Metric Spaces

Exploring Fixed Point Theorems and Metric Structures in Generalized Modular Metric Spaces

Abstract

In this Paper, we first give a new fixed point theorem which is main theorem of our study in modular metric spaces. After that, by using this theorem, we express some interesting results. Moreover, we characterize completeness in modular metric spaces via this theorem. The aim of this paper is to prove the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings defined on generalized metric spaces with a graph. In this work, we discuss the definition of the Reich contraction single or multivalued mappings defined in a modular metric space. In our investigation, we prove the existence of fixed point results for these mappings. In this paper, we introduce a new concept of generalized modular metric space. Then we present some examples showing that the generalized modular metric space includes some kind of metric structures.