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  • 1 Universitatea Babeş-Bolyai Facultatea de Matematicą Str. Kogąlniceanu Nr. 1 RO-3400 Cluj-Napoca Romania
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Abstract  

RecentlyPrus-Wiśniowski [14] has proved that the continuous functions of Λ-bounded variation on [0, 1] form a set of the first category in the Banach space C[0, 1] and also in each Banach space CΓBV[0, 1] of continuous functions of Γ-bounded variation on [0, 1] provided that the sequence Γ is adequate. In the present paper these results are extended and completed by using a principle of the condensation of the singularities of a family of nonnegative functions that follows from the theorems given byBreckner [3]. It is shown that Baire category properties similar to those stated in [14] are valid for two very large classes of real-valued functions called functions of bounded λ-variation of orderp and functions of boundedmth variation of orderp, respectively. The benefit of considering these classes is that they comprise several classes of functions of bounded variation type which have occurred so far in Fourier analysis or real analysis; in particular, the functions investigated in [14]. Thus, by specializing the results derived in the present paper, they give at once Baire category information concerning a number of well-known sets of real-valued functions.

  • Impact Factor (2019): 0.527
  • Scimago Journal Rank (2019): 0.384
  • SJR Hirsch-Index (2019): 15
  • SJR Quartile Score (2019): Q3 Analysis
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.702
  • Scimago Journal Rank (2018): 0.47
  • SJR Hirsch-Index (2018): 14
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Analysis Mathematica
Language English
Size B5
Year of
Foundation
1975
Volumes
per Year
1
Issues
per Year
4
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)