@article { author = {Fallahi, Kamal and Savic, Dragan and Soleimani Rad, Ghasem}, title = {The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application}, journal = {Sahand Communications in Mathematical Analysis}, volume = {13}, number = {1}, pages = {1-15}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.89571.471}, abstract = {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.}, keywords = {$b$-metric space,$wt$-distance,Fixed point,Orbitally $G$-continuous mapping}, url = {https://scma.maragheh.ac.ir/article_34322.html}, eprint = {https://scma.maragheh.ac.ir/article_34322_c1a6f4a5bb424cbcce7290bf293886ca.pdf} }