Strong convergence of a new hybrid iterative method for equilibrium problems and variational inequality problems for nonexpansive mappings in Hilbert spaces
You Xian-hua · Fuzhou daxue xuebao. Ziran kexue ban · 2014
In this paper,we introduce a general iterative scheme for finding a common element of the set of common solutions of generalized equilibrium problems,the set of solutions of a variational inequality and the set of fixed points of nonexpansive mappings in a real Hilbert space. Strong convergence theorems are established in a real Hilbert space under suitable conditions. Then,we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results presented improve and extend the corresponding results of many others.