Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions
Lu-Chuan Ceng, Chi-Ming Chen, Ching‐Feng Wen, Chin-Tzong Pang · Abstract and Applied Analysis · 2014
We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.