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Mat. Zametki, 1972, Volume 12, Issue 5, Pages 523–530 (Mi mz9912)  

This article is cited in 2 scientific papers (total in 2 papers)

Functions of bounded $p$-variation with given order of modulus of $p$-continuity

A. P. Terekhin

Saratov State University

Abstract: We construct continuous functions for which the modulus of $p$-continuity tends to zero with given order in Wiener's sense
$$ V^p(\delta;f)=\sup\sum_i|f(x_i)-f(x_{i-1})|^p\qquad(p>1) $$
(the upper bound is taken over partitions satisfying the condition $x_i-x_{i-1}\leqslant\delta$).

Full text: PDF file (617 kB)

English version:
Mathematical Notes, 1972, 12:5, 751–755

Bibliographic databases:

UDC: 517.5
Received: 30.06.1971

Citation: A. P. Terekhin, “Functions of bounded $p$-variation with given order of modulus of $p$-continuity”, Mat. Zametki, 12:5 (1972), 523–530; Math. Notes, 12:5 (1972), 751–755

Citation in format AMSBIB
\Bibitem{Ter72}
\by A.~P.~Terekhin
\paper Functions of bounded $p$-variation with given order of modulus of $p$-continuity
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 5
\pages 523--530
\mathnet{http://mi.mathnet.ru/mz9912}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318416}
\zmath{https://zbmath.org/?q=an:0242.26002}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 5
\pages 751--755
\crossref{https://doi.org/10.1007/BF01099058}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Volosivets, “Approximation of functions of bounded $p$-variation by means of polynomials of the Haar and Walsh systems”, Math. Notes, 53:6 (1993), 569–575  mathnet  crossref  mathscinet  zmath  isi  elib
    2. S. S. Volosivets, “Approximation of functions of bounded $p$-variation by polynomials in terms of the Faber–Schauder system”, Math. Notes, 62:3 (1997), 306–313  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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