Best Proximity Coincidence Point Results for α , D -Proximal Generalized Geraghty Mappings in J S -Metric Spaces

Abstract

We introduce a type of Geraghty contractions in a $JS$ -metric space $X,$ called $\left(\alpha ,D\right)$ -proximal generalized Geraghty mappings. By using the triangular- $\left(\alpha ,D\right)$ -proximal admissible property, we obtain the existence and uniqueness theorem of best proximity coincidence points for these mappings together with some corollaries and illustrative examples. As an application, we give a best proximity coincidence point result in $X$ endowed with a binary relation.