Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces |
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Authors: | W.M. Kozlowski |
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Affiliation: | School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia |
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Abstract: | Let X be a uniformly convex Banach space with the Opial property. Let T:C→C be an asymptotic pointwise nonexpansive mapping, where C is bounded, closed and convex subset of X. In this paper, we prove that the generalized Mann and Ishikawa processes converge weakly to a fixed point of T. In addition, we prove that for compact asymptotic pointwise nonexpansive mappings acting in uniformly convex Banach spaces, both processes converge strongly to a fixed point. |
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Keywords: | Fixed point Asymptotic pointwise nonexpansive mapping Fixed point iteration process Uniformly convex Banach space Opial property |
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