General iterative algorithms for mixed equilibrium problems, variational inequalities and fixed point problems

Abstract

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a mixed equilibrium problem, a general system of variational inequalities and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild 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

Hybrid viscosity methods for equilibrium problems, variational inequalities, and fixed point problems

“…; See, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”

Algorithms for common solutions of generalized mixed equilibrium problems and system of variational inclusion problems

“…During the last decade, many authors proposed different kinds of algorithms to find the common solutions of some problems mentioned above; See, for example, [13,15,23,25,26] and the references therein.…”