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

Poom Kumam and Chirasak Mongkolkeha
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Poom Kumam: Theoretical and Computational Science (TaCS) Center & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Chirasak Mongkolkeha: Department of Mathematics Statistics and Computer Science, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand

Mathematics, 2019, vol. 7, issue 1, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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