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## Archive of Issues

Russia Izhevsk
Year
2016
Volume
26
Issue
3
Pages
366-378
 Section Mathematics Title On the Riemann-Stieltjes double integral Author(-s) Fedorov D.L.a Affiliations Udmurt State Universitya Abstract 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. Keywords curvilinear integral, double integral, Riemann-Stieltjes integral UDC 517.37 MSC 26A42 DOI 10.20537/vm160306 Received 1 August 2016 Language Russian Citation 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. References Schwabik S., Tvrdy M., Vejvoda O. Differential and integral equations: Boundary value problems and adjoints, Prague: Academia, 1979, 249 p. Derr V.Ya. Teoriya funktsii deistvitel'noi peremennoi. Lektsii i uprazhneniya (Theory of functions of a real variable. Lectures and exercises), Moscow: Vysshaya shkola, 2008, 384 p. Natanson I.P. Teoriya funktsii veshchestvennoi peremennoi (Theory of functions of a real variable), Moscow: Nauka, 1974, 480 p. Riesz F., Szökefalvi-Nagy B. Lektsii po funktsional'nomu analizu (Lectures on functional analysis), Moscow: Mir, 1979, 589 p. Tolstov G.P. Mera i integral (The measure and the integral), Moscow: Nauka, 1976, 392 p. 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 Full text