Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces

Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by {x"0=x@?Carbitrarily chosen ,y"n=@b"nx"n+(1-@b"n)W"nx"n,x"n"+"1=@a"nf(x"n)+(1-@a"n)y"n,@?n>=0, where f is a contraction on C and W"n is a mapping generated by an infinite family of nonexpansive mappings {T"i}"i"="1^~. Assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty. In this paper, we prove that the sequence {x"n} generated by the above iterative algorithm converges strongly to a common fixed point of {T"i}"i"="1^~, which solves some variational inequality. Our results improve and extend the results announced by many others.

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