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On O’Malley preponderantly continuous functions

  • Stanisław Kowalczyk EMAIL logo
Published/Copyright: April 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In the paper some algebraic properties of functions which are preponderantly continuous in O'Malley sense and functions satisfying property A1 are studied. The maximal additive class, the maximal multiplicative class and the maximal class with respect to minimums for these families of functions are described.

Key words: preponderant density; preponderant continuity; maximal additive class; maximal multiplicative class; maximal class with respect to maximums
MSC: Primary 26A99; Secondary 26A15

  1. This paper has been communicated by Wladyslaw Wilczynski

References

[1] Bruckner, A. M.: Differentation of Real Functions. Lecture Notes in Math. 659, Springer, Berlin-New York 1978.10.1007/BFb0069821Search in Google Scholar

[2] Grande Z.: Une remarque sur les fonctions surpassement continues, Rev. Roumaine Math. Pures Appl. 28 (1983), 485–487.Search in Google Scholar

[3] Kowalczyk S.: On preponderantly continuous functions, Pr. Nauk. Akad. Jana Długosza Częst. Mat. 14 (2009), 75–86.Search in Google Scholar

[4] O'Malley R. J.: Note about preponderantly continuous functions, Rev. Roumaine Math. Pures Appl. 21 (1976), 335–336.Search in Google Scholar

[5] Szczuka P.: Macimums of extra strong Świ\c{a}tkowski functions, Math. Slovaca 62 (2012), 473–478.10.2478/s12175-012-0023-zSearch in Google Scholar

Received: 2012-10-23
Accepted: 2013-7-30
Published Online: 2016-4-30
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0120
Keywords for this article
preponderant density; preponderant continuity; maximal additive class; maximal multiplicative class; maximal class with respect to maximums

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  4. On the number of slim, semimodular lattices
  5. Research Article
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  13. Research Article
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