On the level sum of two convex functions on Banach spaces.
Traoré, S., Volle, M. (1996)
Journal of Convex Analysis
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Displaying similar documents to “-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation.”
On the level sum of two convex functions on Banach spaces.
On the p-drop theorem, 1 ≤ p ≤∞.
Abdelhakim Maaden (2002)
Extracta Mathematicae
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Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...
On some aspects of Jensen-Menger convexity.
Joanna Ger, Roman Ger (1992)
Stochastica
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The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.
On equivalent strictly G-convex renormings of Banach spaces
Nataliia Boyko (2010)
Open Mathematics
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We study strictly G-convex renormings and extensions of strictly G-convex norms on Banach spaces. We prove that ℓω(Γ) space cannot be strictly G-convex renormed given Γ is uncountable and G is bounded and separable.
S-rationally convex domains and the approximation of Silva-holomorphic functions by S-rational functions
Paques, O.W., Zaine, M.C. (1990)
Portugaliae mathematica
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A class of spaces lacking normal structure
W. L. Bynum (1972)
Compositio Mathematica
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A note on singular points of convex functions in Banach spaces
Luděk Zajíček (1993)
Acta Universitatis Carolinae. Mathematica et Physica
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On Bárány's theorems of Carathéodory and Helly type
Ehrhard Behrends (2000)
Studia Mathematica
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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...
Recognizing the topology of the space of closed convex subsets of a Banach space
Taras Banakh, Ivan Hetman, Katsuro Sakai (2013)
Studia Mathematica
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