Maximal classes for rho-upper continuous functions

• Autorzy: Kowalczyk S. , Nowakowska K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present some properties of ρ-upper continuous functions. We give a condition equivalent to ρ-upper continuity and find maximal additive and maximal multiplicative classes for the family of ρ-upper continuous functions. These classes depend on whether ρ<1 or ρ=1. To describe maximal additive and maximal multiplicative classes for 1-upper continuous function, we need the notions of sparsity and T*topology.

Słowa kluczowe

EN

density of set at a point; continuous functions; measurable function; path continuity; rho-upper continuous functions

PL

gęstość zbioru w punkcie; funkcja ciągła; funkcja mierzalna; ciągłość ścieżki

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2013
• Tom: Vol. 19, nr 1
• Strony: 69--89
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Kowalczyk S.

• Institute of Mathematics, Academia Pomeraniensis, ul. Arciszewskiego 22b, 76-200 Słupsk, Poland

autor

Nowakowska K.

• Institute of Mathematics, Academia Pomeraniensis, ul. Arciszewskiego 22b, 76-200 Słupsk, Poland

Bibliografia

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• [3] S. Kowalczyk and K. Nowakowska, A note on ρ-upper continuous functions, Tatra Mt. Math. Publ. 44 (2009), 153-158.
• [4] S. Kowalczyk and K. Nowakowska, Maximal classes for the family of [λ,ρ-continuous functions, Real Anal. Exchange 36 (2010/11), 307-324.
• [5] D. N. Sharkel and A. K. De, The proximally continuous integrals, J. Aust. Math. Soc. (A) 31 (1981), 26-45.
• [6] B. S. Thomson, Real Functions, Lecture Notes in Math. 1170, Springer, Berlin, 1985.