Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2015; 52(2): 373-388

Printed March 1, 2015

https://doi.org/10.4134/JKMS.2015.52.2.373

Copyright © The Korean Mathematical Society.

A parallel hybrid method for equilibrium problems, variational inequalities and nonexpansive mappings in Hilbert space

Dang Van Hieu

Hanoi University of Science

Abstract

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

Keywords: hybrid method, equilibrium problem, variational inequality, parallel computation

MSC numbers: 65Y05, 47H09, 47H10, 47J20