$ b-(\varphi, \Gamma)-$graphic contraction on metric space endowed with a graph

Subject Areas : Fixed point theory

Sh. Mirzaee ¹ (Department of Mathematics, Karaj Branch, Islamic Azad University, Alborz, Iran)
M. Eshaghi Gordji ² (Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran)

Received: 2018-05-21 Accepted : 2018-09-12 Published : 2018-09-01

Keywords: fixed point, Metric space, $ b-(\varphi, \Gamma)-$graphic contraction,

Abstract :

In this paper, we introduce the $ b-(\varphi, \Gamma)-$graphic contraction on metric space endowed with a graph so that $(M,\delta)$ is a metric space, and $V(\Gamma)$ is the vertices of $\Gamma$ coincides with $M$. We aim to obtain some new fixed-point results for such contractions. We give an example to show that our results generalize some known results.

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