A Shrinking Projection Method for Generalized Mixed Equilibrium Problems, Variational Inclusion Problems and a Finite Family of Quasi-Nonexpansive Mappings
1 Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
2 Centre of Excellence in Mathematics CHE, Si Ayutthaya Road, Bangkok 10140, Thailand
3 Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin (RMUTR), Bangkok 10100, Thailand
4 Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
Journal of Inequalities and Applications 2010, 2010:458247 doi:10.1155/2010/458247Published: 14 July 2010
The purpose of this paper is to consider a shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of fixed points of a finite family of quasi-nonexpansive mappings, and the set of solutions of variational inclusion problems. Then, we prove a strong convergence theorem of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng et al. (2008), Takahashi et al. (2008), S.Takahashi and W. Takahashi (2008), and many others.