Document Type : Original Article

Authors

• Azizollah Babakhani ¹
• Sami H. Jasem ²
• Sayyed Hashem Rasouli ³

¹ Babol Noshirvani University of Technology

² Department of Mathematics, Babol Noshirvani University of Technology

³ Department of Mathematics, Babol Noshirvani University of Technology, Babol-Iran

Abstract

We consider the $G-$ metric space with including the $P-$property which are introduced by Z. Mustafa and B. Sims (Nonlinear Convex Anal. 7 (2006) 289-297) and presented by B. Samet and et al. in a metric space (Nonlinear Anal. 4 (75) (2012) 2154--2165) respectively. In the present work we define $P-$property in a $G-$ metric space and proved that under which various conditions there exist a best proximity point for non-self‐mapping in $G-$metric space. Also, we introduced for a certain such mappings which its best proximity point is unique under further conditions.

Keywords

• Best proximity point
• \alpha-\psi-proximal contractive
• G-metric space