A new iterative algorithm of solution for equilibrium problems, variational inequalities and fixed point problems in a Hilbert space
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Publication Details
Author list: Katchang P., Kumam P.
Publisher: Springer
Publication year: 2010
Journal: Journal of Applied Mathematics and Computing (1598-5865)
Volume number: 32
Issue number: 1
Start page: 19
End page: 38
Number of pages: 20
ISSN: 1598-5865
eISSN: 1865-2085
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, we introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for β-inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in a Hilbert space. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. As applications, at the end of paper we utilize our results to study some convergence problem for finding the zeros of maximal monotone operators. Our results are generalizations and extensions of the results of Yao and Liou (Fixed Point Theory Appl. Article ID 384629, 10 p., 2008), Yao et al. (J. Nonlinear Convex Anal. 9(2):239-248, 2008) and Su and Li (Appl. Math. Comput. 181(1):332-341, 2006) and some recent results. © 2009 Korean Society for Computational and Applied Mathematics.
Keywords
Viscosity approximation method
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