Abstract
In this paper, by asymptotic center techniques, we shown that the set of fixed points of a uniformly k-lipschitzian semigroup (one-parameter or left reversible semi-topological) in a uniformly convex Banach space is a retract of the domain if k is close to 1. The results presented in this paper includes (among others, in the discrete situation) many known results as special cases.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Górnicki, J. The structure of fixed-point sets of uniformly lipschitzian semigroups. Collect. Math. 63, 333–344 (2012). https://doi.org/10.1007/s13348-011-0040-1
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DOI: https://doi.org/10.1007/s13348-011-0040-1
Keywords
- One-parameter semigroup
- Left reversible semigroup
- Uniformly lipschitzian semigroup
- Retraction
- Asymptotic center
- Fixed point
- Uniformly convex Banach space