Displaying similar documents to “Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces”

On nested sequences of convex sets in Banach spaces

Jesús M. F. Castillo, Manuel González, Pier Luigi Papini (2014)

Studia Mathematica

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We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.

Paraconvex functions and paraconvex sets

Huynh Van Ngai, Jean-Paul Penot (2008)

Studia Mathematica

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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....

The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny (1994)

Studia Mathematica

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Conditions under which the inf-convolution of f and g f □ g ( x ) : = i n f y + z = x ( f ( y ) + g ( z ) ) has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions f : X → ℝ ∪ + ∞ on a reflexive Banach space such that l i m ∥ x ∥ → ∞ f ( x ) / ∥ x ∥ = ∞ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.

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...