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Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {Ti}i=1Ã¢ÂˆÂž be an infinite countable family of asymptotically nonexpansive mappings with the sequence {kin} satisfying kinÃ¢Â‰Â¥1 for each i=1,2,Ã¢Â€Â¦, n=1,2,Ã¢Â€Â¦, and limnÃ¢Â†Â’Ã¢ÂˆÂžkin=1 for each i=1,2,Ã¢Â€Â¦. In this paper, we introduce a new implicit iterative scheme generated by {Ti}i=1Ã¢ÂˆÂž and prove that  the scheme converges strongly to a common fixed point of {Ti}i=1Ã¢ÂˆÂž, which solves some certain variational inequality

An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces