Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings

摘要

We introduce a new iterative scheme by shrinking projection method for finding a commonelement of the set of solutions of generalized mixed equilibrium problems, the set of common solutions ofvariational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotonemappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixedpoints for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove thatthe sequence converges strongly to a common element of the above four sets under some mind conditions.Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem wasobtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu(2011), Zhang et al. (2008), and many authors.