The Existence Theorem for Contractive Mappings on wt-distance in b-metric Spaces Endowed with a Graph and its Application

In this paper, we study the existence and uniqueness of xed points for mappings with respect to a wt-distance in b- metric spaces endowed with a graph. Our results are signi cant, since we replace the condition of continuity of mapping with the condition of orbitally G-continuity of mapping and we consider b- metric spaces with graph instead of b-metric spaces, under which can be generalized, improved, enriched and uni ed a number of recently announced results in the existing literature. Additionally, we elicit all of our main results by a non-trivial example and pose an interesting two open problems for the enthusiastic readers.