STRONG CONVERGENCE THEOREMS FOR GENERALIZED EQUILIBRIUM PROBLEMS AND STRICT PSEUDO-CONTRACTIONS

Abstract

Let {S}_{i=1}^N be N strict pseudo-contractions dened on a closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the fixed point set of these mappings and the solution set of generalized equilibrium problems by parallel and cyclic algorithms. In this paper, we propose new iterative schemes for solving this problem and prove these schemes converge strongly by monotone hybrid methods.