A GENERAL ITERATIVE ALGORITHM COMBINING VISCOSITY METHOD WITH PARALLEL METHOD FOR MIXED EQUILIBRIUM PROBLEMS FOR A FAMILY OF STRICT PSEUDO-CONTRACTIONS y
Thanyarat Jitpeera, Issara Inchan, Poom Kumam · Journal of applied mathematics & informatics · 2011
The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of -strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of -strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.