Structure of the fixed-point set of mappings with lipschitzian iterates
Keywords
Retraction, asymptotic center, fixed point, uniformly convex Banach space, strongly ergodic matrixAbstract
We prove, by asymptotic center techniques and some inequalities in Banach spaces, that if $E$ is $p$-uniformly convex Banach space, $C$ is a nonempty bounded closed convex subset of $E$, and $T\colon C\rightarrow C$ has lipschitzian iterates (with some restrictions), then the set of fixed-points is not only connected but even a retract of $C$. The results presented in this paper improve and extend some results in [J. Górnicki, < i> A remark on fixed point theorems for lipschitzian mappings< /i> , J. Math. Anal. Appl. < b> 183< /b> (1994), 495–508], [J. Górnicki, < i> The methods of Hilbert spaces and structure of the fixed-point set of lipschitzian mapping< /i> , Fixed Point Theory and Applications, Hindawi Publ. Corporation, 2009, Article ID 586487].Downloads
Published
2010-04-23
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1.
GÓRNICKI, Jarosław. Structure of the fixed-point set of mappings with lipschitzian iterates. Topological Methods in Nonlinear Analysis. Online. 23 April 2010. Vol. 36, no. 2, pp. 381 - 393. [Accessed 29 March 2024].
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