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Let C be a nonempty closed convex subset of a Banach space E and let {Sn} be a family of nonexpansive mappings of C into itself such that the set of common fixed points of {Sn} is nonempty. We first introduce a sequence {xn} of C defined by x1=x∈C and xn+1=αnf(xn)+(1−αn)Snxnfor alln∈N, where {αn}⊂(0,1) and f is a contraction of C into itself. Further, we give the conditions of {αn} and {Sn} under...
Let C be a nonempty closed convex subset of a real Banach space X whose norm is uniformly Gâteaux differentiable and T:C→C be a continuous pseudo-contraction with a nonempty fixed point set F(T). For arbitrary given element u∈C and for t∈(0,1), let {yt} be the unique continuous path such that yt=(1−t)Tyt+tu. Assume that yt→p∈F(T) as t→0. Let {αn},{βn} and {γn} be three real sequences in (0, 1) satisfying...
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