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Section
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Mathematics
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Title
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On the Riemann-Stieltjes double integral
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Author(-s)
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Fedorov D.L.a
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Affiliations
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Udmurt State Universitya
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Abstract
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The article deals with the new properties of the Riemann-Stieltjes curvilinear integral. It is proved that the Riemann-Stieltjes curvilinear integral is independent of path of integration if an integrable and an integrating functions depend only on one variable. A new necessary condition of the functional dependence of functions of two variables is found. The author proposes a new approach to the definition of the Riemann-Stieltjes double integral, which contains not one but two integrating functions. General properties of the Riemann-Stieltjes double integral are discussed. Methods for calculating the double integral for the case of smooth or piecewise-smooth integrating functions are presented. A formula for the conversion of the Riemann-Stieltjes double integral into an iterated integral is obtained.
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Keywords
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curvilinear integral, double integral, Riemann-Stieltjes integral
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UDC
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517.37
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MSC
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26A42
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DOI
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10.20537/vm160306
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Received
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1 August 2016
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Language
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Russian
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Citation
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Fedorov D.L. On the Riemann-Stieltjes double integral, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 366-378.
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References
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- Fedorov D.L. On the line contour Riemann-Stiltjes integral, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 3, pp. 117-126 (in Russian). DOI: 10.20537/vm110311
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Full text
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