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http://dx.doi.org/10.7858/eamj.2010.26.1.025

A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS

Zhang, Lijuan (COLLEGE OF MATHEMATICS AND COMPUTER HEBEI UNIVERSITY)
Chen, Jun-Min (COLLEGE OF MATHEMATICS AND COMPUTER HEBEI UNIVERSITY)

Publication Information

East Asian mathematical journal / v.26, no.1, 2010 , pp. 25-38 More about this Journal

Abstract

In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.

Keywords

mixed equilibrium problems; nonexpansive mapping; hybrid iterative schemes; fixed points; inverse-strongly monotone;

Citations & Related Records

Reference

1	L. C. Ceng and J. C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed points problems, J. Comput. Appl. Math. (2008), no. 214 (1), 186-201. DOI ScienceOn
2	F. E. Browder and W. V. Petryshyn, Construction of Fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. (1967), no. 20, 197-228. DOI
3	H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. (2005), no. 613, 341-350.
4	H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl.(2003), no. 116, 659-678. DOI ScienceOn
5	R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. (1970), no. 149, 75-88. DOI ScienceOn
6	T. Suziki, Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl.(2005), no. 305, 227-239. DOI ScienceOn
7	W. Takahashi and K. Shimoji, Convergence theorems for nonexpansive mappings and feasibility problems, Math. Comput. Model. (2000), no. 32, 1463-1471. DOI ScienceOn