Antiproximinal ѕets in Banach ѕpaces
S. Cobzaş (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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S. Cobzaş (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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Traoré, S., Volle, M. (1996)
Journal of Convex Analysis
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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. ...
Soltanov, Kamal N. (2007)
Fixed Point Theory and Applications [electronic only]
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Filipsson, Lars (2006)
International Journal of Mathematics and Mathematical Sciences
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Taras Banakh, Ivan Hetman, Katsuro Sakai (2013)
Studia Mathematica
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Hoang Tu Y
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CONTENTSIntroduction............................................................................................................................................................................... 5§ 1. Finite systems of convex inequalities.......................................................................................................................... 6§ 2. Infinite systems of convex inequalities...........................................................................................................................
Ladislav Forgáč (1976)
Mathematica Slovaca
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Avery, Richard, Henderson, Johnny, O'Regan, Donal (2007)
Fixed Point Theory and Applications [electronic only]
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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.