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In this paper, we introduce new implicit and explicit iterative schemes whichconverge strongly to a unique solution of variational inequality problems forstrongly accretive operators over a common fixed point set of finite family ofnonexpansive mappings in $q$-uniformly smooth real Banach spaces. As anapplication, we introduce an iteration process which converges strongly to asolution of the variational inequality which is a common fixed point of finitefamily 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 ourmethod of proof are of independent interest.

Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods