Coincidence Best Proximity Point Theorems for $(\alpha,g)$-Geraghty Contractive Mappings in Metric Spaces without an Isometry of a Mapping g

Chalongchai Klanarong

Abstract

In this work, we introduce new concepts of a pair of mappings, called  $(\alpha,g)$-proximal admissible, triangular $(\alpha,g)$-proximal admissible and $(\alpha,g)$-Geraghty contractive mappings. By using these types of mappings, we prove the existence and uniqueness of  a coincidence best proximity point in complete metric spaces without an isometry of the mapping $g$. Moreover, we give an  example for our main result. And also, Our main result is a generalization of some well-known results in the literature.