$S$-metric and fixed point theorem

Subject Areas : Fixed point theory

M. Simkhah Asil ¹ , Sh. Sedghi ² , N. Shobe ³ , Z. Mitrovic ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Qaemshar Branch, Islamic Azad University, Qaemshar, Iran
3 - Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran
4 - Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina

Received: 2020-05-18 Accepted : 2020-07-15 Published : 2020-09-01

Keywords: fixed point, implicit relation,

Abstract :

In this paper, we prove a general fixed point theorem in$\textrm{S}$-metric spaces for maps satisfying an implicitrelation on complete metric spaces. As applications, we get manyanalogues of fixed point theorems in metric spaces for$\textrm{S}$-metric spaces.

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