Hybrid Algorithms for Minimization Problems over the Solutions of Generalized Mixed Equilibrium and Variational Inclusion Problems

摘要

We introduce a new general hybrid iterative algorithm for finding a commonelement of the set of solution of fixed point for a nonexpansive mapping, the set of solution ofgeneralized mixed equilibrium problem, and the set of solution of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence convergesstrongly to a common element of the above three sets under some mild conditions. Our results improveand extend the corresponding results of Marino and Xu (2006), Yao and Liou (2010), Tan and Chang(2011), and other authors.