A GENERAL COMPOSITE ITERATIVE METHOD FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS
We introduce a new general composite iterative sheme by the viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert spaces. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping, which is the unique solution of a ceratin variational inquality. Our results substantially develop and improve the corresponding results of Jung [J. S. Jung, Strong convergence of composite iterative methods for equilibrium problems and fixed point problems in Hilber spaces, J. Math. Anal, Apple 336 (2007) 455-469], Shang et al. [M. Shang, X. Qin, Y. Sn, A general iterative method for equilibrium problems and fixed point problems, Fixed Point Theory Appl. (2007), Article ID 64306, 7 pages] and Takahashi and Takahashi [A. Takahashi and W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilber space, J. Math. Anal. appl. 333(2007) 506-515].
equilibrium problem fixed points viscosity approximation method nonexpansive mapping composite iterative scheme variational inequality contraction