Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces
Siwaporn Saewan, Poom Kumam, Yeol Je Cho · Journal of Inequalities and Applications · 2013
In this paper, we construct a new hybrid projection method for approximating a common element of the set of zeroes of a finite family of maximal monotone operators and the set of common solutions to a system of generalized equilibrium problems in a uniformly smooth and strictly convex Banach space. We prove strong convergence theorems of the algorithm to a common element of these two sets. As application, we also apply our results to find common solutions of variational inequalities and zeroes of maximal monotone operators. MSC: 47H05, 47H09, 47H10.