Weak and strong convergence of hybrid subgradient method for pseudomonotone equilibrium problem and multivalued nonexpansive mappings
Dao-Jun Wen · Fixed Point Theory and Applications · 2014
In this paper, we introduce a hybrid subgradient method for finding a common element of the set of solutions of a class of pseudomonotone equilibrium problems and the set of fixed points of a finite family of multivalued nonexpansive mappings in Hilbert space. The proposed method involves only one projection rather than two as in the existing extragradient method and the inexact subgradient method for an equilibrium problem. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. Moreover, a numerical example is given to illustrate our algorithm and our results. MSC:47H05, 47H09, 47H10.