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Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator F:xn=αnγV(xn)+βnxn-1+((1-βn)I-αnμF)Tnxn and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.