mann iterates of directionally nonexpansive mappings in hyperbolic spaces

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ID: 208787
2003
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Abstract
In a previous paper, the first author derived an explicit quantitative version of a theorem due to Borwein, Reich, and Shafrir on the asymptotic behaviour of Mann iterations of nonexpansive mappings of convex sets C in normed linear spaces. This quantitative version, which was obtained by a logical analysis of the ineffective proof given by Borwein, Reich, and Shafrir, could be used to obtain strong uniform bounds on the asymptotic regularity of such iterations in the case of bounded C and even weaker conditions. In this paper, we extend these results to hyperbolic spaces and directionally nonexpansive mappings. In particular, we obtain significantly stronger and more general forms of the main results of a recent paper by W. A. Kirk with explicit bounds. As a special feature of our approach, which is based on logical analysis instead of functional analysis, no functional analytic embeddings are needed to obtain our uniformity results which contain all previously known results of this kind as special cases.
Reference Key
kohlenbach2003abstractmann Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Ulrich Kohlenbach;Laurentiu Leustean
Journal science and technology of advanced materials
Year 2003
DOI
10.1155/S1085337503212021
URL
http://dx.doi.org/10.1155/S1085337503212021
Keywords
mathematics

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