Convex inequalities and the Hahn-Banach Theorem

Hoang Tu Y

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Antiproximinal ѕets in Banach ѕpaces

S. Cobzaş (1999)

Acta Universitatis Carolinae. Mathematica et Physica

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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. ...

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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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.