General iterative algorithms for mixed equilibrium problems, a general system of generalized equilibria and fixed point problems
Huiying Hu, Lu-Chuan Ceng, Yanlai Song · Journal of Inequalities and Applications · 2014
Abstract In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. MSC:49J30, 47H10, 47H15.