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Relevant bibliographies by topics / Riemann integral. Integrals, Stieltjes

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Journal articles

Academic literature on the topic 'Riemann integral. Integrals, Stieltjes'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Riemann integral. Integrals, Stieltjes"

1

Gal, Sorin G. "On a Choquet-Stieltjes type integral on intervals." Mathematica Slovaca 69, no. 4 (2019): 801–14. http://dx.doi.org/10.1515/ms-2017-0269.

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Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtain

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2

Narita, Keiko, Kazuhisa Nakasho, and Yasunari Shidama. "Riemann-Stieltjes Integral." Formalized Mathematics 24, no. 3 (2016): 199–204. http://dx.doi.org/10.1515/forma-2016-0016.

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Abstract In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described the definitions. In the last section, we proved theorems about linearity of Riemann-Stielt

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3

Rumlawang, Francis Y., and Harimanus Batkunde. "SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES." BAREKENG: Jurnal Ilmu Matematika dan Terapan 1, no. 2 (2007): 25–30. http://dx.doi.org/10.30598/barekengvol1iss2pp25-30.

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If is limited and []ℜ→baf,:[]ℜ→ba,:α Monotone increase in [, is Riemann-Stieltjes integral able to α on ] ba,[]ba, simply written by[]αRSf∈ if . With JI=()()xdxfIbaα∫= is called Riemann Stieltjes lower integral f to α and ()()xdxfJbaα∫= is called Riemann Stieltjes upper integral f to α. Then is called Riemann Stieltjes upper integral f to ()()∫==baxdxfJIαα on [. if f ang g is Riemann Stieltjes integralable, and, k oe √ then f + g, kf, and fg is also Riemann Stieltjes integralable. But if f and ] ba,α have united discontinue point then f is not Riemann Stieltjes integralable on α

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4

Ma, Wenjie, Shuman Meng, and Yujun Cui. "Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations." Mathematical Problems in Engineering 2018 (August 7, 2018): 1–8. http://dx.doi.org/10.1155/2018/5438592.

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This paper deals with the following Caputo fractional differential equations with Riemann-Stieltjes integral boundary conditions Dc0+αut=ft,ut,u′t,u′′t, t∈0,1, u0=u′′0=0, u1=∫01‍utdAt, where Dc0+α denotes the standard Caputo derivative, α∈(2,3]; ∫01x(t)dA(t) denotes the Riemann-Stieltjes integrals of x with respect to A. By mean of coincidence degree theory, we obtain the existence of solutions for the above fractional BVP at resonance. In the end, according to the main results, we give a typical example.

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5

Pirade, Septian, Tohap Manurung, and Jullia Titaley. "Integral Riemann-Stieltjes Pada Fungsi Bernilai Real." d'CARTESIAN 6, no. 1 (2017): 1. http://dx.doi.org/10.35799/dc.6.1.2017.14987.

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Integral Riemann-Stieltjes merupakan generalisasi dari Integral Riemann, kedua Integral ini memiliki hubungan, juga beberapa sifat dasar pada Integral Riemann dapat diberlakukan pada Integral Riemann-Stieltjes. Misalkan f dan a adalah fungsi bernilai real yang terbatas pada interval [a,b]. Jika f ϵ R[a,b] dan f ϵ Ra[a,b], maka sifat terbatas, monoton naik, linear penjumlahan dan linear perkalian terhadap konstanta yang berlaku pada fungsi f yang terintegral Riemann, berlaku juga pada fungsi f yang terintegral Riemann-Stieltjes. Jika a(x) = x, maka integral Riemann-Stieltjes ekuivalen dengan in

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6

Bradley, R. E. "The Riemann-Stieltjes Integral." Missouri Journal of Mathematical Sciences 6, no. 1 (1994): 20–28. http://dx.doi.org/10.35834/1994/0601020.

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7

Štajner-Papuga, Ivana, Tatjana Grbić, and Martina Daňková. "Pseudo-Riemann–Stieltjes integral." Information Sciences 179, no. 17 (2009): 2923–33. http://dx.doi.org/10.1016/j.ins.2008.09.009.

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8

Makogin, Vitalii, and Yuliya Mishura. "Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions." Nonlinear Analysis: Modelling and Control 25, no. 6 (2020): 1079–106. http://dx.doi.org/10.15388/namc.2020.25.20566.

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In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under Schauder basis. The class of weighted Takagi–Landsberg functions of order H > 0 on [0; 1] coincides with the class of H-Hölder continuous functions on [0; 1]. Based on computed fractional integrals and derivatives of the Haar and Schauder functions, we get a new series representation of the fractional derivatives of a Hölder continuous funct

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9

LUKKARINEN, JANI, and MIKKO S. PAKKANEN. "ON THE POSITIVITY OF RIEMANN–STIELTJES INTEGRALS." Bulletin of the Australian Mathematical Society 87, no. 3 (2012): 400–405. http://dx.doi.org/10.1017/s0004972712000639.

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10

Yaskov, Pavel. "On pathwise Riemann–Stieltjes integrals." Statistics & Probability Letters 150 (July 2019): 101–7. http://dx.doi.org/10.1016/j.spl.2019.02.005.

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