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Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure
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D. R. Sahu
,
R. P. Agarwal
Published/Copyright:
May 12, 2011
Abstract
This paper is concerned with weak uniformly normal structure and the structure of the set of fixed points of Lipschitzian mappings. It is shown that in a Banach space X with weak uniformly normal structure, every asymptotically regular Lipschitzian semigroup of self-mappings defined on a weakly compact convex subset of X satisfies the (ω)-fixed point property. We show that if X has a uniformly Gâteaux differentiable norm, then the set of fixed points of every asymptotically nonexpansive mapping is nonempty and sunny nonexpansive retract of C. Our results improve several known fixed point theorems for the class of Lipschitzian mappings in a general Banach space.
Keywords.: Nonexpansive mapping; asymptotically nonexpansive mapping; retraction; sunny nonexpansive retraction; common fixed point; weak uniformly normal structure
Received: 2010-02-13
Revised: 2010-04-06
Accepted: 2010-05-11
Published Online: 2011-05-12
Published in Print: 2011-June
© de Gruyter 2011
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Keywords for this article
Nonexpansive mapping;
asymptotically nonexpansive mapping;
retraction;
sunny nonexpansive retraction;
common fixed point;
weak uniformly normal structure
Articles in the same Issue
- Semiinfinite multiobjective fractional programming, part II: Duality models
- Wavelet characterization of Sobolev spaces with variable exponent
- Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure
- Masas in the Calkin algebra without the Continuum Hypothesis
- Existence and uniqueness results of some fractional boundary value problem
- Set-valued variational-like inclusions with H -η-accretive operators in Banach spaces
- On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection
- An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions
- Comparison ODE theorems related to the method of lines
