Mathematics – Functional Analysis
Scientific paper
2010-07-06
Mathematics
Functional Analysis
Scientific paper
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 $q$-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.
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