Noncyclic Meir-Keeler contractions and best proximity pair theorems

Abstract

In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and generalize a main result of Chen [Chen C. M., A note on asymptotic pointwise weaker Meir-Keeler type contractions, Appl. Math. Lett., 2012, 25, 1267-1269]. Examples are given to support our main results.

Keywords

• best proximity pair
• CAT(0) space
• uniformly convex Banach space
• projection mapping
• noncyclic Meir-Keeler contraction
• 47H10
• 47H09
• 46B20