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KYUNGPOOK Math. J. 2019; 59(4): 703-723

Published online December 23, 2019

Copyright © Kyungpook Mathematical Journal.

Hybrid Algorithms for Ky Fan Inequalities and Common Fixed Points of Demicontractive Single-valued and Quasinonexpansive Multi-valued Mappings

Nawitcha Onjai-uea and Withun Phuengrattana∗

Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University, Nakhon Pathom 73000, Thailand
e-mail : nawitcha@hotmail.com and withun_ph@yahoo.com

Received: December 30, 2017; Revised: December 2, 2018; Accepted: December 6, 2018

Abstract

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

Keywords: demicontractive mappings, quasi-nonexpansive mappings, Ky Fan inequality, variational inequality, Hilbert spaces.