$b$-metric spaces with a graph and best proximity points for some contractions

Subject Areas : Fixed point theory

K.  Fallahi ¹ (Department of Mathematics, Payame Noor University, Tehran, Iran)
M.  Ayobian ² (Department of Mathematics, Payame Noor University, Tehran, Iran)

Received: 2021-09-29 Accepted : 2021-11-26 Published : 2021-12-01

Keywords: fixed point, Best proximity point, $G$-continuous mapping,

Abstract :

In this paper, we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph. Then we support our main theorem by a non-trivial example and give some consequences of it for usual graphs.

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