%0 Journal Article
%T The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Fallahi, Kamal
%A Savic, Dragan
%A Soleimani Rad, Ghasem
%D 2019
%\ 02/01/2019
%V 13
%N 1
%P 1-15
%! The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
%K $b$-metric space
%K $wt$-distance
%K Fixed point
%K Orbitally $G$-continuous mapping
%R 10.22130/scma.2018.89571.471
%X In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, 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 unified 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.
%U https://scma.maragheh.ac.ir/article_34322_c1a6f4a5bb424cbcce7290bf293886ca.pdf