A convergence theorem based on a hybrid relaxed extragradient method for generalized equilibrium problems and fixed point problems of a finite family of nonexpansive mappings

A new hybrid algorithm for a system of equilibrium problems and variational inclusion

“…It is easy to see that for any λ constant is in (0, 2β], then the mapping I − λB is nonexpansive, where I is the identity mapping on H. The generalized mixed equilibrium problem include fixed point problems, optimization problems, variational inequalities problems, Nash equilibrium problems, noncooperative games, economics and the equilibrium problems as special cases (see, e.g., [2,8,9,20,22,31]). Some methods have been proposed to solve the equilibrium problem; see, for instance [6,10,[12][13][14][15][16]19,25,29,30].…”