Best proximity point theorems in 1/2−modular metric spaces

Subject Areas : Functional analysis

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

Received: 2018-10-19 Accepted : 2019-02-27 Published : 2019-06-01

Keywords: Best proximity point, (α, Θ)−ω-contractions, 1/2−modular metric space,

Abstract :

‎In this paper‎, ‎first we introduce the notion of $\frac{1}{2}$-modular metric spaces and weak $(\alpha,\Theta)$-$\omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an example to illustrate the usability of these theorems‎.

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