Points of monotonicity in Orlicz–Lorentz function spaces
✍ Scribed by Wanzhong Gong; Zhongrui Shi
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 433 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0362-546X
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📜 SIMILAR VOLUMES
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 Lorentz᎐Orlicz function spaces.
## Abstract Generalized Orlicz‐Lorentz function spaces Λ~φ~ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (cf. 34 and 38) are investigated. A regularity condition \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Delta ^{\Lambd
## Abstract Let Λ~__w,ϕ__~ be the Orlicz–Lorentz space. We study Gateaux differentiability of the functional ψ~__w,ϕ__~ (__f__) = $ \int \_{0} ^{\infty} $ __ϕ__ (__f__ \*)__w__ and of the Luxemburg norm. More precisely, we obtain the one‐sided Gateaux derivatives in both cases and we characterize