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Remarks on the structure of the fixed-point sets of uniformly lipschitzian mappings in uniformly convex Banach spaces
- Source :
-
Journal of Mathematical Analysis & Applications . Jul2009, Vol. 355 Issue 1, p303-310. 8p. - Publication Year :
- 2009
-
Abstract
- Abstract: It is shown, by asymptotic center techniques, that the set of fixed points of any uniformly k-lipschitzian mapping in a uniformly convex Banach space is a retract of the domain when k is less than a constant bigger than the constant from the paper [K. Goebel, W.A. Kirk, A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973) 135–140]. Our result improves a recently result presented in [E. Sędłak, A. Wiśnicki, On the structure of fixed-point sets of uniformly lipschitzian mappings, Topol. Methods Nonlinear Anal. 30 (2007) 345–350]. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 355
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 36816286
- Full Text :
- https://doi.org/10.1016/j.jmaa.2009.02.003