On nowhere density of the class of somewhat continuous functions in
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Tibor Šalát (1978)
Časopis pro pěstování matematiky
Krzysztof Ciesielski, Kandasamy Muthuvel, Andrzej Nowik (2001)
Fundamenta Mathematicae
A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each point x we...
Jean Schmets, Manuel Valdivia (2003)
RACSAM
Si K es un compacto no vacío en Rr, damos una condición suficiente para que la inyección canónica de ε{M},b(K) en ε{M},d(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε{M1}(F)A en ε{M2}(Rr)D donde F es un subconjunto cerrado propio de Rr y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.
Bravyi, Evgeniy I., Gusarenko, Sergey S. (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Aleroev, T.S. (2005)
Sibirskij Matematicheskij Zhurnal
Wu, Yu-Dong (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Hugo Aimar, Raquel Crescimbeni (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Belaidi, Benharrat, El Farissi, Abdallah, Latreuch, Zinelaâbidine (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Wing-Sum Cheung (1989)
Aequationes mathematicae
Cheung, Wing-Sum, Zhao, Chang-Jian (2007)
Journal of Inequalities and Applications [electronic only]
Tord Sjödin (1984)
Annales Polonici Mathematici
Pachpatte, B.G. (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Changjian, Zhao, Cheung, Wing-Sum (2010)
Journal of Inequalities and Applications [electronic only]
Alois Kufner, Herbert Leinfelder (1998)
Mathematica Bohemica
Necessary and sufficient condition on the weights will be derived under which a -th order Hardy inequality holds on classes of functions satisfying more than “boundary” conditions.
Izumino, Saichi, Mori, Hideo, Seo, Yuki (1998)
Journal of Inequalities and Applications [electronic only]
Horst Alzer (2000)
Czechoslovak Mathematical Journal
Let be a real number and let be an even integer. We determine the largest value such that the inequality holds for all real numbers which are pairwise distinct and satisfy . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value in the case and odd, and in the case and even.
Tomasz Natkaniec, Piotr Szuca (2010)
Colloquium Mathematicae
We prove that if f: → is Darboux and has a point of prime period different from , i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.
Changjian, Zhao, Chen, Chur-Jen, Cheung, Wing-Sum (2009)
Journal of Inequalities and Applications [electronic only]
Mercer, A.McD. (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Władysław Wilczyński (1971)
Colloquium Mathematicae