Maximal classes for lower and upper semicontinuous strong Świątkowski functions

• Autorzy: Szczuka P.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions. Moreover, we characterize the maximal class with respect to maximums for lower semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions.

Słowa kluczowe

EN

Darboux function; strong Świątkowski function; lower semicontinuous function; upper semicontinuous function

PL

funkcje Darbouxa; funkcja z silną własnością Świątkowskiego; funkcja półciągła

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 48--55
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Szczuka P.

• Kazimierz Wielki University, pl. Weyssenhoffa 11, 85–072 Bydgoszcz, Poland

Bibliografia

• [1] J. Farková, About the maximum and the minimum of Darboux functions, Matemat. Cas. 21(2) (1971), 110–116.
• [2] R. A. Gordon, The integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics, vol. 4, American Mathematical Society, 1994.
• [3] A. Maliszewski, On the limits of strong Świątkowski functions, Zeszyty Nauk. Politech. Łódz. Mat. 27(719) (1995), 87–93.
• [4] A. Maliszewski, The maximal class with respect to maximums for the family of almost continuous functions, Real Anal. Exchange 32(2) (2006/07), 313–318.
• [5] P. Szczuka, Maximal classes for the family of strong Świątkowski functions, Real Anal. Exchange 28(2) (2002/03), 429–437.
• [6] P. Szczuka, Products of strong Świątkowski functions, J. Appl. Anal. 12(1) (2006), 129–145.
• [7] P. Szczuka, Sums and products of extra strong Świątkowski functions, Tatra Mt. Math. Publ. 49 (2011), 71–79.
• [8] P. Szczuka, The maximal class with respect to maximums for the family of upper semicontinuous strong Świątkowski functions, accepted for publication in Mathematica Slovaca.