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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Methods of comparison of families of real functions in porosity terms

Stanisław KowalczykORCID iD: https://orcid.org/0000-0001-8404-3427 / Małgorzata TurowskaORCID iD: https://orcid.org/0000-0001-9802-7874
Published Online: 2019-05-10 | DOI: https://doi.org/10.1515/gmj-2019-2025


We consider some families of real functions endowed with the metric of uniform convergence. In the main results of our work we present two methods of comparison of families of real functions in porosity terms. The first method is very general and may be applied to any family of real functions. The second one is more convenient but can be used only in the case of path continuous functions. We apply the obtained results to compare in terms of porosity the following families of functions: continuous, absolutely continuous, Baire one, Darboux, also functions of bounded variation and porouscontinuous, ρ-upper continuous, ρ-lower continuous functions.

Keywords: Porosity; strong porosity; path continuity; comparison of families of real functions

MSC 2010: 54C30; 54C08; 54C50


  • [1]

    M. Bienias, S. Gła̧b and W. Wilczyński, Cardinality of sets of ρ-upper and ρ-lower continuous functions, Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform. 64 (2014), no. 2, 71–80. Google Scholar

  • [2]

    J. Borsík and J. Holos, Some properties of porouscontinuous functions, Math. Slovaca 64 (2014), no. 3, 741–750. Web of ScienceGoogle Scholar

  • [3]

    A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, Berlin, 1978. Google Scholar

  • [4]

    A. M. Bruckner, R. J. O’Malley and B. S. Thomson, Path derivatives: A unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), no. 1, 97–125. CrossrefGoogle Scholar

  • [5]

    M. Filipczak, G. Ivanova and J. Wódka, Comparison of some families of real functions in porosity terms, Math. Slovaca 67 (2017), no. 5, 1155–1164. Web of ScienceGoogle Scholar

  • [6]

    T. Filipczak, On some abstract density topologies, Real Anal. Exchange 14 (1988/89), no. 1, 140–166. Google Scholar

  • [7]

    G. Ivanova, A. Karasińska and E. Wagner-Bojakowska, Comparison of some subfamilies of functions having the Baire property, Tatra Mt. Math. Publ. 65 (2016), 151–159. Google Scholar

  • [8]

    G. Ivanova and E. Wagner-Bojakowska, On some subclasses of the family of Darboux Baire 1 functions, Opuscula Math. 34 (2014), no. 4, 777–788. CrossrefGoogle Scholar

  • [9]

    S. Kowalczyk and K. Nowakowska, A note on ϱ-upper continuous functions, Tatra Mt. Math. Publ. 44 (2009), 153–158. Google Scholar

  • [10]

    S. Kowalczyk and K. Nowakowska, A note on the [0]-lower continuous functions, Tatra Mt. Math. Publ. 58 (2014), 111–128. Google Scholar

  • [11]

    S. Kowalczyk and M. Turowska, On structural properties of porouscontinuous functions, Math. Slovaca 67 (2017), no. 5, 1239–1250. Web of ScienceGoogle Scholar

  • [12]

    L. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (1987/88), no. 2, 314–350. Google Scholar

About the article

Received: 2016-12-22

Revised: 2018-03-03

Accepted: 2018-05-21

Published Online: 2019-05-10

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2025.

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