Strong Convergence of a General Iterative Algorithm for Mixed Equilibrium, Variational Inequality and Common Fixed Points Problems

Tanakit Thianwan

Department of Mathematics, School of Science, University of Phayao, Phayao, Thailand.

DOI: 10.4236/apm.2013.31011                

Abstract

The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.

Keywords

Nonexpansive Mapping; Mixed Equilibrium Problem; Variational Inequality; Common Fixed Points; Strong Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

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