Nonexpansive and locally nonexpansive mappings in product spaces
β Scribed by W.A. Kirk; Carlos Martinez Yanez
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 442 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
In this paper, we prove that if Ο is a convex, Ο-finite modular function satisfying a 2 -type condition, C a convex, Ο-bounded, Ο-a.e. compact subset of L Ο , and T C β C a Ο-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map define
We introduce the class of Ξ±-nonexpansive mappings in Banach spaces. This class contains the class of nonexpansive mappings and is related to the class of firmly nonexpansive mappings in Banach spaces. In addition, we obtain a fixed point theorem for Ξ±nonexpansive mappings in uniformly convex Banach