On existence and uniqueness of best proximity points for proximal β-quasi contractive mappings on metric spaces

Abstract

This paper focus on the study of the generalization of the best proximity point theorems for non-self contractions. In fact we propose two new theorems on the existence and the uniqueness of best proximity points for proximal β-quasi contractive mappings on metric spaces . The presented theorems extend and generalize the existence and the uniqueness of best proximity points for proximal contraction done by S.Basha and quasi-contraction mappings performed by Jleli and Samet.