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Asymptotically Nonexpansive Mappings in Modular Function Spaces

✍ Scribed by T. Dominguez-Benavides; M.A. Khamsi; S. Samadi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
121 KB
Volume
265
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper, we prove that if ρ is a convex, Οƒ-finite modular function satisfying a 2 -type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of L ρ , and T C β†’ C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map defined on a convex subset of L 1 Β΅ which is compact for the topology of local convergence in measure has a fixed point.

πŸ“œ SIMILAR VOLUMES

Strong Convergence of Averaged Approxima
Strong Convergence of Averaged Approximants for Asymptotically Nonexpansive Mappings in Banach Spaces
✍ Naoki Shioji; Wataru Takahashi πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 129 KB

Let C be a closed, convex subset of a uniformly convex Banach space whose norm is uniformly Ga^teaux differentiable and let T be an asymptotically nonexpansive mapping from C into itself such that the set F(T ) of fixed points of T is nonempty. In this paper, we show that F(T ) is a sunny, nonexpans