The purpose of this article is to present a general viscosity iteration process{xn}which defined byxn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xnand to study the convergence of{xn}, whereTis a nonexpansive mapping andAis a strongly positive linear operator, if{αn},{βn}satisfy appropriate conditions, then iteration sequence{xn}converges strongly to the unique solutionx*∈f(T)of variational inequality〈(A−γf)x*,x−x*〉≥0,for allx∈f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others.
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