A new iterative scheme with nonexpansive mappings for equilibrium problems
1 Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
2 Department of Mathematics, Haiphong university, Vietnam
Journal of Inequalities and Applications 2012, 2012:116 doi:10.1186/1029-242X-2012-116Published: 28 May 2012
In this paper, we suggest a new iteration scheme for finding a common of the solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed points of a nonexpansive mapping. The scheme is based on both hybrid method and extragradient-type method. We obtain a strong convergence theorem for the sequences generated by these processes in a real Hilbert space. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.
AMS 2010 Mathematics subject classification: 65 K10, 65 K15, 90 C25, 90 C33.