Hybrid methods for a mixed equilibrium problem and fixed points of a countable family of multivalued nonexpansive mappings
Aunyarat Bunyawat, Suthep Suantai · Fixed Point Theory and Applications · 2013
In this paper, we prove a strong convergence theorem for a new hybrid method, using shrinking projection method introduced by Takahashi and a fixed point method for finding a common element of the set of solutions of mixed equilibrium problem and the set of common fixed points of a countable family of multivalued nonexpansive mappings in Hilbert spaces. We also apply our main result to the convex minimization problem and the fixed point problem of a countable family of multivalued nonexpansive mappings. MSC: 47H09, 47H10.