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Vestn. Udmurtsk. Univ. Mat., 2006, Issue 1, Pages 41–62
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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:
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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
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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V. Ya. Derr, D. M. Kinzebulatov, “Ob umnozhenii obobschennykh funktsii”, Izv. IMI UdGU, 2006, no. 2(36), 43–48
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D. M. Kinzebulatov, “Odnostoronnie mery Diraka i igra s razryvnoi funktsiei vyigrysha”, Izv. IMI UdGU, 2006, no. 2(36), 65–68
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V. Ya. Derr, D. M. Kinzebulatov, “Dynamical generalized functions and the multiplication problem”, Russian Math. (Iz. VUZ), 51:5 (2007), 32–43
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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
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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
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V. Ya. Derr, “Differentsialnye uravneniya v algebre $\it{C}$-obobschennykh funktsii”, Tr. IMM UrO RAN, 22, no. 3, 2016, 62–75
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V. Ya. Derr, “O rasshirenii integrala Rimana–Stiltesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 135–152
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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
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