Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods
Functional Analysis
2010-07-07 v1
Abstract
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of nonexpansive mappings in -uniformly smooth real Banach spaces. As an application, we introduce an iteration process which converges strongly to a solution of the variational inequality which is a common fixed point of finite family of strictly pseudocontractive mappings. Our theorems extend, generalize, improve and unify the corresponding results of Xu \cite{27} and Yamada \cite{Yamada} and that of a host of other authors. Our corollaries and our method of proof are of independent interest.
Cite
@article{arxiv.1007.0941,
title = {Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods},
author = {Eric U. Ofoedu},
journal= {arXiv preprint arXiv:1007.0941},
year = {2010}
}