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In this paper, we introduce three new iterative methods for finding a commonpoint of the set of fixed points of a symmetric generalized hybrid mapping andthe set of solutions of an equilibrium problem in a real Hilbert space. Eachmethod can be considered as an combination of Ishikawa's process with theproximal point algorithm, the extragradient algorithm with or withoutlinesearch. Under certain conditions on parameters, the iteration sequencesgenerated by the proposed methods are proved to be weakly convergent to asolution of the problem. These results extend the previous results given in theliterature. A numerical example is also provided to illustrate the proposedalgorithms.

Weak convergence theorems for a symmetric generalized hybrid mapping and an equilibrium problem