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Strong convergence theorems for nonexpansive semigroup in Banach spaces |
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| Authors: | Yisheng Song Sumei Xu |
| Affiliation: | a College of Mathematics and Information Science, Henan Normal University, 453007, China b Department of Mathematics and Applied Mathematics, Anyang Normal University, PR China |
| Abstract: | Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, and  a nonexpansive self-mappings semigroup of K, and  a fixed contractive mapping. The strongly convergent theorems of the following implicit and explicit viscosity iterative schemes {xn} are proved.xn=αnf(xn)+(1−αn)T(tn)xn, |
| Keywords: | Nonexpansive semigroup Viscosity approximation methods Reflexive and strictly convex Banach space Chebyshev set |
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