Existence of common best proximity points of generalized $S$-proximal contractions

Document Type: Research Paper


1 Department of Mathematics, Texas A & M University-Kingsville-78363-8202, Texas, USA

2 University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia


In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend some results existing in the literature.