Convergence to common solutions of various problems for nonexpansive mappings in Hilbert spaces
Kyung Soo Kim · Fixed Point Theory and Applications · 2012
Nonlinear Anal.70:4195-4208, 2009), we introduce a new iterative scheme for finding a common element of the set of solutions of a mixed equilibrium problem for an equilibrium bifunction, the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of some variational inequality problem, and the set of fixed points of a left amenable semigroup {T t : t ∈ S} of nonexpansive mappings with respect to W-mappings and a left regular sequence {μ n } of means defined on an appropriate space of bounded real-valued functions of the semigroup S. Furthermore, we prove that the iterative scheme converges strongly to a common element of the above four sets.Our results extend and improve the corresponding results of many others.