Document Type: Research Paper
Authors
- Kamal Fallahi ^{} ^{} ^{1}
- Dragan Savic ^{2}
- Ghasem Soleimani Rad ^{} ^{1}
^{1} Department of Mathematics, Payame Noor University, Tehran, Iran.
^{2} Primary School ''Kneginja Milica", Beograd, Serbia.
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
Main Subjects
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