IJPAM: Volume 82, No. 2 (2013)

HYBRID ITERATIVE METHOD FOR A GENERAL SYSTEM
OF VARIATIONAL INEQUALITIES IN HILBERT
SPACES WITH APPLICATIONS

S. Imnang
Department of Mathematics and Statistics
Faculty of Science
Thaksin University
Phatthalung Campus, Phatthalung, 93110, THAILAND
and
Centre of Excellence in Mathematics, CHE
Si Ayutthaya Road, Bangkok 10400, THAILAND


Abstract. The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a general system of variational inequality problems for $\alpha$-inverse-strongly monotone mappings, the set of solutions of mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Furthermore, we apply our main result with the problem of approximating a zero of a finite family of maximal monotone mappings in Hilbert spaces. Our main result extends and improves the recent results of Ceng, Wang and Yao [#!5.2!#] and many others.

Received: September 20, 2012

AMS Subject Classification: 47H10, 49J40, 47H05, 47H09, 46B20.

Key Words and Phrases: nonexpansive mapping, general system of variational inequality problem, mixed equilibrium problem, demi-closedness principle

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 2