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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Poom Kumam & Chirasak Mongkolkeha, 2019. "Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions," Mathematics, MDPI, vol. 7(1), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:46-:d:195012
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    References listed on IDEAS

    as
    1. A. Abkar & M. Gabeleh, 2012. "Global Optimal Solutions of Noncyclic Mappings in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 298-305, May.
    2. Chirasak Mongkolkeha & Poom Kumam, 2012. "Best Proximity Point Theorems for Generalized Cyclic Contractions in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 215-226, October.
    3. Rafael Espínola & G. Sankara Raju Kosuru & P. Veeramani, 2015. "Pythagorean Property and Best-Proximity Point Theorems," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 534-550, February.
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