A hybrid projection method for solving a common solution of a system of equilibrium problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense in Hilbert spaces
1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok, 10140, Thailand
2 Department of Mathematics, Faculty of Education, Bansomdejchaopraya Rajabhat University (BSRU), Thonburi, Bangkok, 10600, Thailand
Journal of Inequalities and Applications 2012, 2012:252 doi:10.1186/1029-242X-2012-252Published: 30 October 2012
In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding a common solution of a system of equilibrium problems of bifunctions satisfying certain conditions and a common solution of fixed point problems of a family of uniformly Lipschitz continuous and asymptotically -strict pseudocontractive mappings in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give a numerical example which supports our results.
MSC: 47H05, 47H09, 47H10.