Existence of best proximity and fixed points in $G_p$-metric spaces

Subject Areas : Fixed point theory

S.  Rathee ¹ (Department of Mathematics, Maharshi Dayanand University, Rohtak, India)
K.  Dhingra ² (Department of Mathematics, Maharshi Dayanand University, Rohtak, India)

Received: 2017-10-13 Accepted : 2018-07-07 Published : 2018-09-01

Keywords: fixed point, $G_p$-metric space, orbital admissible mapping,

Abstract :

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spaces. We also provide examples to analyze and support our results.

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