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Nonexpansive maps in Orlicz spaces

✍ Scribed by Dozo, E. Lami


Publisher
Springer-Verlag
Year
1985
Weight
183 KB
Volume
55
Category
Article
ISSN
0370-7377

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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 define

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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