Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings

Abstract

In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their common best proximity point. Next, we put forward the concept of multivalued Kannan-type contractive pair and also the concept of weak Δ-property to determine the existence of common best proximity point for such a pair of maps.

Keywords

• common best proximity point
• fixed point
• contraction map
• complete metric space
• multivalued map
• optimization