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Remarks on the structure of the fixed-point sets of uniformly lipschitzian mappings in uniformly convex Banach spaces

Authors :
Górnicki, Jarosław
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