Uniformly convex and uniformly smooth convex functions
Dominique Azé, Jean-Paul Penot (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Dominique Azé, Jean-Paul Penot (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Jacek Tabor, Józef Tabor, Krzysztof Misztal (2013)
Banach Center Publications
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There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.
Penot, Jean-Paul (2005)
Journal of Inequalities and Applications [electronic only]
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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.
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