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Let E be a real q-uniformly smooth Banach space with constant dq, qÃ¢Â‰Â¥2. Let T:EÃ¢Â†Â’E and G:EÃ¢Â†Â’E be a nonexpansive map and an ÃŽÂ·-strongly accretive map which is also ÃŽÂº-Lipschitzian, respectively. Let {ÃŽÂ»n} be a real sequence in [0,1] that satisfies the following condition: C1:limÃŽÂ»n=0 and Ã¢ÂˆÂ‘ÃŽÂ»n=Ã¢ÂˆÂž. For ÃŽÂ´Ã¢ÂˆÂˆ(0,(qÃŽÂ·/dqkq)1/(qÃ¢ÂˆÂ’1)) and ÃÂƒÃ¢ÂˆÂˆ(0,1), define a sequence {xn} iteratively in E by x0Ã¢ÂˆÂˆE,   xn+1=TÃŽÂ»n+1xn=(1Ã¢ÂˆÂ’ÃÂƒ)xn+ÃÂƒ[TxnÃ¢ÂˆÂ’ÃŽÂ´ÃŽÂ»n+1G(Txn)], nÃ¢Â‰Â¥0. Then, {xn} converges strongly to the unique solution x* of the variational inequality problem VI(G,K) (search for x*Ã¢ÂˆÂˆK such that Ã¢ÂŒÂ©Gx*,jq(yÃ¢ÂˆÂ’x*)Ã¢ÂŒÂªÃ¢Â‰Â¥0 for all yÃ¢ÂˆÂˆK), where K:=Fix(T)={xÃ¢ÂˆÂˆE:Tx=x}Ã¢Â‰Â Ã¢ÂˆÂ…. A convergence theorem related to finite family of nonexpansive maps is also proved

Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities