Nelson Merentes (1991)
Collectanea Mathematica
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Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
Yung-Ming Chen (1964)
Studia Mathematica
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Pawel Kolwicz, Ryszard Pluciennik (1997)
Collectanea Mathematica
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Ye Yining, Huang Yafeng (1993)
Collectanea Mathematica
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We prove that in the Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, P-convexity coincides with reflexivity.
Pawel. Kolwicz, Ryszard Pluciennik (1998)
Revista Matemática Complutense
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It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.
Charles Cleaver (1972)
Studia Mathematica
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Yunan Cui, Henryk Hudzik, Wang Ping (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Johann Boos, Toivo Leiger (1989)
Studia Mathematica
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Bor-Luh Lin, Zhongrui Shi (1999)
Colloquium Mathematicae
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We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.
Shutao Chen, Huiying Sun (1994)
Studia Mathematica
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We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
Zhongdao Ren, Shutao Chen (1997)
Collectanea Mathematica
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Estimation of the Jung constants of Orlicz function spaces equipped with either Luxemburg norm or Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz function spaces have been found by using a new quantitative index of N-functions.