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Vestn. Udmurtsk. Univ. Mat., 2006, Issue 1, Pages 41–62 (Mi vuu245)  

This article is cited in 7 scientific papers (total in 8 papers)

MATHEMATICS

The Alpha-integral of Stieltjes type

V. Ya. Derra, D. M. Kinzebulatovb

a Udmurt State University, Izhevsk
b Izhevsk State Technical University

Abstract: The equivalence classes of regulated functions, which differ only on the points of discontinuity, are considered. On these classes the integral of Riemann–Stieltjes is extenced; one modification of Perron–Stieltjes integral (called alpha-integral) is introduced for them. The integration by parts theorem, the substitution theorem, the change of order of integration theorem, the convergence theorems for these integrals are proved.

Full text: PDF file (524 kB)
UDC: 517.2; 517.5
Received: 01.10.2005

Citation: V. Ya. Derr, D. M. Kinzebulatov, “The Alpha-integral of Stieltjes type”, Vestn. Udmurtsk. Univ. Mat., 2006, no. 1, 41–62

Citation in format AMSBIB
\Bibitem{DerKin06}
\by V.~Ya.~Derr, D.~M.~Kinzebulatov
\paper The Alpha-integral of Stieltjes type
\jour Vestn. Udmurtsk. Univ. Mat.
\yr 2006
\issue 1
\pages 41--62
\mathnet{http://mi.mathnet.ru/vuu245}


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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. V. Ya. Derr, D. M. Kinzebulatov, “Ob umnozhenii obobschennykh funktsii”, Izv. IMI UdGU, 2006, no. 2(36), 43–48  mathnet
    2. D. M. Kinzebulatov, “Odnostoronnie mery Diraka i igra s razryvnoi funktsiei vyigrysha”, Izv. IMI UdGU, 2006, no. 2(36), 65–68  mathnet
    3. V. Ya. Derr, D. M. Kinzebulatov, “Dynamical generalized functions and the multiplication problem”, Russian Math. (Iz. VUZ), 51:5 (2007), 32–43  mathnet  crossref  mathscinet  zmath
    4. S. D. Buntov, N. I. Leonov, E. L. Tonkov, N. N. Petrov, A. A. Gryzlov, B. P. Kondratev, A. I. Karpov, A. V. Borisov, D. L. Fedorov, “Vasilii Yakovlevich Derr. K yubileyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 1, 133–136  mathnet
    5. V. Ya. Derr, I. G. Kim, “Prostranstvo pravilnykh funktsii i differentsialnoe uravnenie s obobschennymi funktsiyami v koeffitsientakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 1, 3–18  mathnet
    6. V. Ya. Derr, “Differentsialnye uravneniya v algebre $\it{C}$-obobschennykh funktsii”, Tr. IMM UrO RAN, 22, no. 3, 2016, 62–75  mathnet  crossref  mathscinet  elib
    7. V. Ya. Derr, “O rasshirenii integrala Rimana–Stiltesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 135–152  mathnet  crossref  elib
    8. Fedorov D.L., Gryzlov A.A., Kinzebulatov D.M., Latypova N.V., Maksimov V.P., Petrov N.N., Popova S.N., Rodionov V.I., Rodina L.I., Smetanin Yu.M., Zaitsev V.A., “Vasilii Yakovlevich Derr. to Anniversary”, Vestn. Udmurt. Univ.-Mat. Mekh. Kompyuternye Nauk., 29:4 (2019), 612–617  crossref  isi
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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