Nonexpansive maps in Orlicz spaces
β Scribed by Dozo, E. Lami
- Publisher
- Springer-Verlag
- Year
- 1985
- Weight
- 183 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0370-7377
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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
It is shown that if l . is an Orlicz sequence space, then the space l w 1 (l . ) of weakly summable sequences in l . is continuously embedded into l . (l 2 ) (resp., into l . (l . )) whenever t [ .(-t) is equivalent to a concave function (resp., a convex function and . is a supermultiplicative funct