University of GuilanComputational Sciences and Engineering2783-2503Articles in Press20240121On a best proximity point theorems for \alpha,d_{G}-regular contractive type mappings in G-metric spaces746210.22124/cse.2024.26472.1071ENAzizollahBabakhaniBabol Noshirvani University of TechnologySami H.JasemDepartment of Mathematics, Babol Noshirvani University of TechnologySayyed HashemRasouliDepartment of Mathematics, Babol Noshirvani University of Technology, Babol-IranJournal Article20240114We 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-selfâmapping in $G-$metric space. Also, we introduced for a certain such mappings which its best proximity point is unique under further conditions.