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On O’Malley ϱ-upper continuous functions

  • Stanisław Kowalczyk EMAIL logo and Katarzyna Nowakowska
Published/Copyright: June 7, 2017
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Abstract

In the paper we present some properties of functions which are ϱ-upper continuous in O’Malley’s sense. Connections with the standard ϱ-upper continuous functions are studied and the maximal additive class and the maximal multiplicative class for this family of functions are described.

MSC 2010: Primary 26A15; 54C30

(Communicated by Ľubica Holá)


References

[1] Borsík, J.—Holos, J.: Some properties of porouscontinuous functions, Math. Slovaca 64 (2014), 741–750.10.2478/s12175-014-0237-3Search in Google Scholar

[2] Bruckner, A. M.: Differentation of Real Functions. Lecture Notes in Mathematics, Vol. 659, Springer-Verlag Berlin Heidelberg New York, 1978.Search in Google Scholar

[3] Bruckner, A. M.—O’Malley, R. J.—Thomson, B. S.: Path derivatives: A unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), 97–125.10.1090/conm/042/807973Search in Google Scholar

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

[5] Kowalczyk, S.—Nowakowska, K.: A note on ϱ-upper continuous functions, Tatra Mt. Math. Publ. 44 (2009), 153–158.10.2478/v10127-009-0055-0Search in Google Scholar

[6] Kowalczyk, S.—Nowakowska, K.: Maximal classes for ϱ-upper continuous functions, J. Appl. Anal. 19 (2013), 69–89.10.1515/jaa-2013-0005Search in Google Scholar

[7] Kowalczyk, S.—Nowakowska, K.: A note on the [0]-lower continuous functions, Tatra Mt. Math. Publ. 58 (2014), 111–128.10.2478/tmmp-2014-0010Search in Google Scholar

[8] Kowalczyk, S.—Nowakowska, K.: Maximal classes for the family of [λ,ϱ]-continuous functions, Real Anal. Exchange 36 (2010/11), 307–324.10.14321/realanalexch.36.2.0307Search in Google Scholar

[9] O’Malley, R. J.: Note about preponderantly continuous functions, Revue Roumanie Math. Pureed Appl. 21 (1976), 335–336.Search in Google Scholar

Received: 2014-11-12
Accepted: 2015-10-28
Published Online: 2017-6-7
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences

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