APPROXIMATING COMMON ELEMENTS OF THE SET OF AMENABLE SEMIGROUP AND VARIATIONAL INEQUALITY AND INFINITE FAMILY OF NON-EXPANSIVE MAPPINGS AND GENERALIZED MIXED EQUILIBRIUM PROBLEMS
Qiang Li, Jun Li, PR China · 2014
In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed point of an infinite family of non-expansive mappings and left amenable semigroup, the set of solution of generalized mixed equilibrium problem and the set of solutions of the variational inequalities for solving inverse strongly monotone mappings in Hilbert spaces by using a hybrid steepest descent methods. Then strong convergence of the scheme to a common element of the three sets is proved. Our results improve and generalize some well-known results in the literature.