Strong Convergence Theorems for a Generalized Equilibrium Problem with a Relaxed Monotone Mapping and a Countable Family of Nonexpansive Mappings in a Hilbert Space
1 School of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2 Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende, Italy
Fixed Point Theory and Applications 2010, 2010:230304 doi:10.1155/2010/230304Published: 8 July 2010
We introduce a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong convergence theorems in fixed point problems, variational inequalities, and equilibrium problems.