- - - Department of Mathematics, Texas A & M University-Kingsville-۷۸۳۶۳-۸۲۰۲, Texas, USA
- - - University of Belgrade, Faculty of Mathematics, Studentski trg ۱۶, ۱۱۰۰۰ 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.

common best proximity point, optimal approximate solution, proximally commuting mappings