A Hybrid Iterative Scheme for Mixed Equilibrium Problems, General System of Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces. (7th June 2011)

• Record Type: Journal Article
• Authors: Imnang, S.; Suantai, S.
• Other Names: Zhang S. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2011(2011)
• Publication Date: 2011-06-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.5402/2011/837809
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : We introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Using the demiclosedness principle for nonexpansive mappings, we prove that the iterative sequence converges strongly to a common element of the above three sets under some control conditions, and we also give some examples for mappings which satisfy conditions of the main result.