Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions

Abstract

The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, min x ∈ A d ( x , T x ) , min y ∈ B d ( y , T y ) and min ( x , y ) ∈ A × B d ( x , y ) ; also, we provide some illustrative examples to support our results. As an application, the existence of a solution of the analytic complex function is discussed.

Keywords

• best proximity point
• noncyclic mapping
• quasi-noncyclic relatively nonexpansive
• semi-sharp proximal pair