SOME RESULTS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS IN HILBERT SPACES

作者：Cho Yeol Je; Qin Xiaolong^*; Kang Shin Min

来源：Journal of Computational Analysis and Applications, 2009, 11(2): 294-316.

• Nonexpansive mapping
• Viscosity approximation method
• Equilibrium problem
• Fixed point

The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of solutions of a equilibrium problems. Our results improve and extend recent results announced by [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515], [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341-350.] [S. Plubtieng, R. Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 336 (2007) 445-469], [Y. Su, M. Shang, X. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and many others.

• 出版日期2009-4