Iterative approximation of fixed points of nonexpansive mappings |
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Authors: | C.E. Chidume C.O. Chidume |
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Affiliation: | a The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy b Department of Mathematics and Statistics, Auburn University, Auburn, AL, USA |
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Abstract: | Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm and be a nonexpansive mapping with F(T):={x∈K:Tx=x}≠∅. For a fixed δ∈(0,1), define by Sx:=(1−δ)x+δTx, ∀x∈K. Assume that {zt} converges strongly to a fixed point z of T as t→0, where zt is the unique element of K which satisfies zt=tu+(1−t)Tzt for arbitrary u∈K. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: ; . For arbitrary x0∈K, let the sequence {xn} be defined iteratively by xn+1=αnu+(1−αn)Sxn. |
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Keywords: | Uniformly Gâ teaux differentiable norm Uniformly smooth real Banach spaces |
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