The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces

[摘要] We consider a hybrid projection algorithm based on the shrinking projection method for two families of quasi-ϕ-nonexpansive mappings. We establish strong convergence theorems for approximatingthe common element of the set ofthe common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. As applications, at the end of the paper we first apply our results to considerthe problem of finding a zero point of an inverse-strongly monotone operatorandwe finally utilize our results to studythe problem of finding a solution of the complementarity problem.Our results improve and extend the corresponding results announced by recent results.

[发布日期] 2009-11-04