Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings

Abstract: Let C be a nonempty closed convex subset of a real strictly convex and reflexive Banach space E which has a uniformly Gâteaux differentiable norm. Let be a given contractive mapping and be an infinite family of nonexpansive mappings such that the common fixed point sets . Let and be two real sequences in [0,1]. For given arbitrarily, let the sequence be generated iteratively bywhere is the W-mapping generated by the mappings and . Suppose the iterative parameters and satisfy the following control conditions: [(C1)] ; [(C2)] ; [(B5)] . Then the sequence converges strongly to where p is the unique solution in F to the following variational inequality: [Copyright &y& Elsevier]