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Displaying 421 – 440 of 882

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On nowhere weakly symmetric functions and functions with two-element range

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...

On nuclear maps between spaces of ultradiferentiables jets of Roumieu type.

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}.

On open problems of F. Qi.

Belaidi, Benharrat, El Farissi, Abdallah, Latreuch, Zinelaâbidine (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On overdetermined Hardy inequalities

Alois Kufner, Herbert Leinfelder (1998)

Mathematica Bohemica

Necessary and sufficient condition on the weights will be derived under which a k -th order Hardy inequality holds on classes of functions satisfying more than k “boundary” conditions.

On Ozeki's inequality.

Izumino, Saichi, Mori, Hideo, Seo, Yuki (1998)

Journal of Inequalities and Applications [electronic only]

On Ozeki’s inequality for power sums

Horst Alzer (2000)

Czechoslovak Mathematical Journal

Let p ( 0 , 1 ) be a real number and let n 2 be an even integer. We determine the largest value c n ( p ) such that the inequality i = 1 n | a i | p c n ( p ) holds for all real numbers a 1 , ... , a n which are pairwise distinct and satisfy min i j | a i - a j | = 1 . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value c n ( p ) in the case p > 0 and n odd, and in the case p 1 and n even.

On Pawlak's problem concerning entropy of almost continuous functions

Tomasz Natkaniec, Piotr Szuca (2010)

Colloquium Mathematicae

We prove that if f: → is Darboux and has a point of prime period different from 2 i , 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.

Currently displaying 421 – 440 of 882