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http://dx.doi.org/10.5666/KMJ.2019.59.4.703

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

Onjai-uea, Nawitcha (Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University)
Phuengrattana, Withun (Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 703-723 More about this Journal
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;
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