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Some Generalizations of Locally Uniform Rotundity

โœ Scribed by P Bandyopadhyay; Da Huang; Bor-Luh Lin; S.L Troyanski

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
90 KB
Volume
252
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Some new generalizations of locally uniform rotundity in Banach spaces are introduced and studied.

๐Ÿ“œ SIMILAR VOLUMES

k-Uniform Rotundity of Lorentzโ€“Orlicz Sp
k-Uniform Rotundity of Lorentzโ€“Orlicz Spaces
โœ Pei-Kee Lin ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 192 KB

It is known that if an Orlicz function space is k-uniformly rotund for some k G 2, then it must be uniformly convex. In the paper, we show that a similar result holds in LorentzแŽOrlicz function spaces.

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## Abstract Necessary and sufficient conditions are given for weak uniform rotundity of Orlicz sequence spaces equipped with the Luxemburg norm.

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We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess [15] and the ultradifferentiable functions in the sense of Braun et al. [4]. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving al