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Relevant bibliographies by topics / Riemann-Stieltjes integral

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Academic literature on the topic 'Riemann-Stieltjes integral'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 April 2022

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Journal articles on the topic "Riemann-Stieltjes integral"

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Rumlawang, Francis Y., and Harimanus Batkunde. "SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES." BAREKENG: Jurnal Ilmu Matematika dan Terapan 1, no. 2 (December 1, 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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Narita, Keiko, Kazuhisa Nakasho, and Yasunari Shidama. "Riemann-Stieltjes Integral." Formalized Mathematics 24, no. 3 (September 1, 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-Stieltjes integral. Because there are two types of linearity in Riemann-Stieltjes integral, we proved linearity in two ways. We showed the proof of theorems based on the description of the article [7]. These formalizations are based on [8], [5], [3], and [4].

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Pirade, Septian, Tohap Manurung, and Jullia Titaley. "Integral Riemann-Stieltjes Pada Fungsi Bernilai Real." d'CARTESIAN 6, no. 1 (February 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 integral Riemann, dan dapat direduksi menjadi integral Riemann ketika a mempunyai turunan dan terbatas pada interval terbuka (a,b). Kata kunci : Fungsi Bernilai Real, Integral Riemann, Integral Riemann-Stieltjes.

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

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

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Wu, Hsien-Chung. "The Fuzzy Riemann-Stieltjes Integral." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 01 (February 1998): 51–67. http://dx.doi.org/10.1142/s0218488598000045.

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In the classcial sense, the expectation is sometimes defined as Riemann-Stieltjes integral. In this paper, we propose the concept of fuzzy Riemann-Stieltjes integral to make the expectation of fuzzy random variable applicable to statistical analysis for imprecise data.

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Muchtar, Kalfin, Jullia Titaley, and Mans Mananohas. "Integral Baire-1 Stieltjes, Henstock-Stieltjes dan Riemann-Stieltjes." d'CARTESIAN 5, no. 1 (April 29, 2016): 7. http://dx.doi.org/10.35799/dc.5.1.2016.11937.

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Beberapa sifat dasar termasuk Kriteria Cauchy dan Teorema Aditif dapat diberlakukan pada konsep integral Baire-1 Stieltjes. Misalkan 𝑓 dan 𝑔 merupakan fungsi-fungsi bernilai real yang didefinisikan pada [𝑎,𝑏]⊂ℝ. Jika 𝑓 terintegral Baire-1 Stieltjes terhadap 𝑔 pada [𝑎,𝑏], maka 𝑓 terintegral Henstock-Stieltjes terhadap 𝑔 pada [𝑎,𝑏] dengan nilai integralnya sama. Syarat cukup agar fungsi 𝑓 yang terintegral Henstock-Stieltjes terhadap 𝑔 pada [𝑎,𝑏] terintegral Baire-1 Stieltjes terhadap 𝑔 pada [𝑎,𝑏] yaitu 𝑓 fungsi kelas Baire-1 dan 𝑔 fungsi bervariasi terbatas pada [𝑎,𝑏]. Jika 𝑓 terintegral Riemann-Stieltjes terhadap fungsi 𝑔 pada [𝑎,𝑏], maka 𝑓 terintegral Baire-1 Stieltjes terhadap 𝑔 pada [𝑎,𝑏] dengan nilai integralnya sama. Kata Kunci: Integral Baire-1 Stieltjes, Integral Henstock-Stieltjes, Integral Riemann-Stieltjes

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Zhao, Weijing, and Zhaoning Zhang. "Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/874651.

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The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.

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Rodionov, V. I. "The adjoint Riemann-Stieltjes integral." Russian Mathematics 51, no. 2 (February 2007): 75–79. http://dx.doi.org/10.3103/s1066369x07020107.

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Pfeffer. "THE GENERALIZED RIEMANN-STIELTJES INTEGRAL." Real Analysis Exchange 21, no. 2 (1995): 521. http://dx.doi.org/10.2307/44152664.

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Dissertations / Theses on the topic "Riemann-Stieltjes integral"

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Chiu, Mei Choi. "General Riemann-Stieltjes integrals /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?MATH%202002%20CHIU.

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Manço, Rafael de Freitas. "Integrais e aplicações." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-30112016-154343/.

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O intuito deste trabalho é fazer uma análise sobre o processo de integração de funções. Existem muitas generalizações do conceito de integração abordado inicialmente por meio da integral de Riemann, como por exemplo, a integral de Riemann-Stieltjes, Lebesgue, Henstock-Kurzweil entre outras. Abordaremos especialmente a integral de Riemann-Stieltjes, e mostraremos a limitação da integral de Riemann no estudo de convergência de funções, indicando a necessidade de se generalizar o processo de integração. Faremos uma aplicação da integral de Riemann-Stieltjes no estudo de variáveis aleatórias e apresentamos uma proposta de abordagem, para a sala de aula, sobre o deslocamento e distância percorrida por um objeto em movimento retilíneo uniforme associado a área.
The aim of this work is analizing the process of integration of functions. There are many generalizations of the integration concept originally addressed by Riemann integral such as the Riemann-Stieltjes integral, Lebesgue integral, Henstock-Kurzweil integral, among others. We will be specially concerned with the integral of Riemann-Stieltjes and we will show the limitations of Riemann integral about convergence of functions, leading to the need to generalize the integration process. We will apply Riemann-Stieltjes integral for the study of random variables and present an approach to the classroom, on the displacement and distance traveled by an object in uniform rectilinear motion associated to concept of area.

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Leffler, Klara. "The Riemann-Stieltjes integral : and some applications in complex analysis and probability theory." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-89199.

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The purpose of this essay is to prove the existence of the Riemann-Stieltjes integral. After doing so, we present some applications in complex analysis, where we define the complex curve integral as a special case of the Riemann- Stieltjes integral, and then focus on Cauchy’s celebrated integral theorem. To show the versatility of the Riemann-Stieltjes integral, we also present some applications in probability theory, where the integral generates a general formula for the expectation, regardless of its underlying distribution.

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Larsson, David. "Generalized Riemann Integration : Killing Two Birds with One Stone?" Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-96661.

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Since the time of Cauchy, integration theory has in the main been an attempt to regain the Eden of Newton. In that idyllic time [. . . ] derivatives and integrals were [. . . ] different aspects of the same thing. -Peter Bullen, as quoted in [24] The theory of integration has gone through many changes in the past centuries and, in particular, there has been a tension between the Riemann and the Lebesgue approach to integration. Riemann's definition is often the first integral to be introduced in undergraduate studies, while Lebesgue's integral is more powerful but also more complicated and its methods are often postponed until graduate or advanced undergraduate studies. The integral presented in this paper is due to the work of Ralph Henstock and Jaroslav Kurzweil. By a simple exchange of the criterion for integrability in Riemann's definition a powerful integral with many properties of the Lebesgue integral was found. Further, the generalized Riemann integral expands the class of integrable functions with respect to Lebesgue integrals, while there is a characterization of the Lebesgue integral in terms of absolute integrability. As this definition expands the class of functions beyond absolutely integrable functions, some theorems become more cumbersome to prove in contrast to elegant results in Lebesgue's theory and some important properties in composition are lost. Further, it is not as easily abstracted as the Lebesgue integral. Therefore, the generalized Riemann integral should be thought of as a complement to Lebesgue's definition and not as a replacement.
Ända sedan Cauchys tid har integrationsteori i huvudsak varit ett försök att åter finna Newtons Eden. Under den idylliska perioden [. . . ] var derivator och integraler [. . . ] olika sidor av samma mynt.-Peter Bullen, citerad i [24] Under de senaste århundradena har integrationsteori genomgått många förändringar och framförallt har det funnits en spänning mellan Riemanns och Lebesgues respektive angreppssätt till integration. Riemanns definition är ofta den första integral som möter en student pa grundutbildningen, medan Lebesgues integral är kraftfullare. Eftersom Lebesgues definition är mer komplicerad introduceras den först i forskarutbildnings- eller avancerade grundutbildningskurser. Integralen som framställs i det här examensarbetet utvecklades av Ralph Henstock och Jaroslav Kurzweil. Genom att på ett enkelt sätt ändra kriteriet for integrerbarhet i Riemanns definition finner vi en kraftfull integral med många av Lebesgueintegralens egenskaper. Vidare utvidgar den generaliserade Riemannintegralen klassen av integrerbara funktioner i jämförelse med Lebesgueintegralen, medan vi samtidigt erhåller en karaktärisering av Lebesgueintegralen i termer av absolutintegrerbarhet. Eftersom klassen av generaliserat Riemannintegrerbara funktioner är större än de absolutintegrerbara funktionerna blir vissa satser mer omständiga att bevisa i jämforelse med eleganta resultat i Lebesgues teori. Därtill förloras vissa viktiga egenskaper vid sammansättning av funktioner och även möjligheten till abstraktion försvåras. Integralen ska alltså ses som ett komplement till Lebesgues definition och inte en ersättning.

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Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.

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Mestrado em Mathematical Finance
O objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de soluções. O resultado, original desta dissertação, é aplicado a um modelo Vasicek fraccionário de taxas de juro.
This dissertation aims to generalize a result on the exponential stability of trivial solutions of stochastic differential equations driven by the fractional Brownian motion by Garrido-Atienza et al. to non-trivial solutions in the scalar case. Notions on fractional calculus are presented, as well as the definition and main properties of the fractional Brownian motion. Subsequently the framework for SDEs driven by fractional Brownian motion with a pathwise approach is characterized along with some existence and uniqueness results. The result on stability is then applied to the fractional Vasicek model for interest rates.
info:eu-repo/semantics/publishedVersion

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Santos, Leandro Nunes dos [UNESP]. "As integrais de Riemann, Riemann-Stieltjes e Lebesgue." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/94350.

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Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-07-26Bitstream added on 2014-06-13T19:34:55Z : No. of bitstreams: 1 santos_ln_me_rcla_parcial.pdf: 254454 bytes, checksum: e32c8bbf83212b9a080a05b6df96f529 (MD5) Bitstreams deleted on 2015-06-25T13:00:45Z: santos_ln_me_rcla_parcial.pdf,. Added 1 bitstream(s) on 2015-06-25T13:03:12Z : No. of bitstreams: 1 000719346_20160726.pdf: 224220 bytes, checksum: 33187ebbdf2a29afe4f365dc6ce932e7 (MD5) Bitstreams deleted on 2016-07-29T12:53:55Z: 000719346_20160726.pdf,. Added 1 bitstream(s) on 2016-07-29T12:54:49Z : No. of bitstreams: 1 000719346.pdf: 949531 bytes, checksum: f249fa8a2707372138d0d3be07ff83fd (MD5)
Este trabalho apresenta resultados importantes sobre a Teoria de Integração. Inicialmente é desenvolvida uma parte sobre Teoria da Medida, necessária para introduzir a integral de Lebesgue e suas propriedades. Também é apresentada a integral de Riemann-Stieltjes. Em seguida, são demonstrados resultados importantes sobre converg ência envolvendo as integrais de Lebesgue, resultados estes que não são válidos para integrais de Riemann. Para apresentar tais temas, usa-se mais fortemente as referências [1], [2], [3] e [4]
This study presents important results on Integration of Theory. The rst of all part is developed on Measure Theory which is necessary to introduce the Lebesgue integral and its properties and we introduce. It also shows the Riemann-Stieltjes integral. Important results are proved on convergence involving the integrals of Lebesgue, which are not valid for the Riemann integral. Im order to present these themes we strongly use the references [1], [2], [3] and [4]

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Santos, Leandro Nunes dos. "As integrais de Riemann, Riemann-Stieltjes e Lebesgue /." Rio Claro, 2013. http://hdl.handle.net/11449/94350.

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Orientador: Marta Cilene Gadotti
Banca: Paulo Leandro Dattori da Silva
Banca: Ricardo Parreira da Silva
Resumo: Este trabalho apresenta resultados importantes sobre a Teoria de Integração. Inicialmente é desenvolvida uma parte sobre Teoria da Medida, necessária para introduzir a integral de Lebesgue e suas propriedades. Também é apresentada a integral de Riemann-Stieltjes. Em seguida, são demonstrados resultados importantes sobre converg ência envolvendo as integrais de Lebesgue, resultados estes que não são válidos para integrais de Riemann. Para apresentar tais temas, usa-se mais fortemente as referências [1], [2], [3] e [4]
Abstract: This study presents important results on Integration of Theory. The rst of all part is developed on Measure Theory which is necessary to introduce the Lebesgue integral and its properties and we introduce. It also shows the Riemann-Stieltjes integral. Important results are proved on convergence involving the integrals of Lebesgue, which are not valid for the Riemann integral. Im order to present these themes we strongly use the references [1], [2], [3] and [4]
Mestre

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Giorgetti, Matteo. "Integrale di Riemann-Stieltjes e applicazioni a processi stocastici di Poisson." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1566/.

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Addamiano, Laura. "L'integrale di Stieltjes e suoi sviluppi." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/800/.

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Books on the topic "Riemann-Stieltjes integral"

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Dragomir, Silvestru Sever. Riemann–Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle. CRC Press, 2019. http://dx.doi.org/10.1201/9780429326950.

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Riemann-Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle: With Applications to Unitary Operators in Hilbert Spaces. Taylor & Francis Group, 2019.

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Dragomir, Silvestru Sever. Riemann-Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle: With Applications to Unitary Operators in Hilbert Spaces. Taylor & Francis Group, 2019.

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Segundo Curso sobre Elementos Básicos del Análisis Matemático. UJAT, 2021. http://dx.doi.org/10.19136/book.189.

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Este libro puede servir como guía en la impartición de un curso semestral de Análisis Matemático para estudiantes universitarios con conocimientos básicos sobre cálculo diferencial e integral de Riemann para funciones de una variable, así como de convergencia y continuidad de espacios métricos. El libro consiste de cuatro capítulos, en los cuales se abordan los siguientes temas: integración de Riemann-Stieltjes, convergencia puntual y uniforme de sucesiones y series de funciones, teoría de diferenciación e integración de Riemann para funciones de varias variables e integración impropia de Riemann. En todos estos temas se dan demostraciones muy detalladas de los resultados y se presentan varios ejemplos que coadyuvan a la comprensión y uso de los conceptos y resultados presentados. Cada sección contiene una lista de ejercicios que pueden ser resueltos con sólo el material previo y el de la sección correspondiente. Tales listas contienen ejercicios que se resuelven o demuestran en forma más o menos directa de las definiciones y teoremas vistos, y algunos no en forma tan directa, pero se presentan sugerencias para algunos de los más intricados. Estas listas de ejercicios son además un complemento de la teoría vista en las secciones, pues varios de ellos corresponden a demostrar algunas proposiciones o corolarios que se desprenden de algunos teoremas importantes; así como a demostrar algunas afirmaciones en las pruebas de estos teoremas, lo cual induce al estudiante a realizar un análisis cuidadoso de tales demostraciones y adquirir una mejor comprensión de tales teoremas.

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Book chapters on the topic "Riemann-Stieltjes integral"

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Bartle, Robert. "Riemann-Stieltjes integral." In Graduate Studies in Mathematics, 391–99. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/gsm/032/28.

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Kaczor, W. J., and M. T. Nowak. "The Riemann-Stieltjes integral." In The Student Mathematical Library, 3–57. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/stml/021/01.

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Kaczor, W. J., and M. T. Nowak. "The Riemann-Stieltjes integral." In The Student Mathematical Library, 97–246. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/stml/021/03.

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Rubel, Lee A., and James E. Colliander. "The Riemann-Stieltjes Integral." In Entire and Meromorphic Functions, 3–5. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0735-1_2.

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Lang, Serge. "Riemann-Stieltjes Integral and Measure." In Real and Functional Analysis, 278–94. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0897-6_10.

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Mackevičius, Vigirdas. "Other Definitions: Riemann and Stieltjes Integrals." In Integral and Measure, 59–78. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781119037514.ch5.

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Walter, Wolfgang. "Das Riemann-Stieltjes-Integral. Kurven- und Wegintegrale." In Grundwissen Mathematik, 190–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-96792-4_6.

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Walter, Wolfgang. "Das Riemann-Stieltjes-Integral. Kurven- und Wegintegrale." In Springer-Lehrbuch, 190–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-55922-8_6.

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Walter, Wolfgang. "Das Riemann-Stieltjes-Integral. Kurven- und Wegintegrale." In Grundwissen Mathematik, 190–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-97366-6_6.

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Walter, Wolfgang. "Das Riemann-Stieltjes-Integral. Kurven- und Wegintegrale." In Springer-Lehrbuch, 190–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-97614-8_6.

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Conference papers on the topic "Riemann-Stieltjes integral"

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Stajner-Papuga, Ivana, Tatjana Grbic, and Martina Dankova. "A note on pseudo Riemann-Stieltjes integral." In 2007 5th International Symposium on Intelligent Systems and Informatics. IEEE, 2007. http://dx.doi.org/10.1109/sisy.2007.4342627.

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Ren, Xue-kun, Cong-xin Wu, and Zhi-gang Zhu. "A New Kind of Fuzzy Riemann-Stieltjes Integral." In 2006 International Conference on Machine Learning and Cybernetics. IEEE, 2006. http://dx.doi.org/10.1109/icmlc.2006.259056.

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Jawarneh, Y. M., and M. S. M. Noorani. "The Beesack-Darst-Poolard inequality for Riemann-Stieltjes double integral." In THE 2013 UKM FST POSTGRADUATE COLLOQUIUM: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2013 Postgraduate Colloquium. AIP Publishing LLC, 2013. http://dx.doi.org/10.1063/1.4858788.

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CERONE, P., and S. S. DRAGOMIR. "NEW BOUNDS FOR THE THREE-POINT RULE INVOLVING THE RIEMANN-STIELTJES INTEGRAL." In Proceedings of the Wollongong Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776372_0006.

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Dragomir, Sever S., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Accurate Approximations of the Riemann-Stieltjes Integral with (l,L)-Lipschitzian Integrators." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790242.

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Manjuram, R., and V. Muthulakshmi. "Oscillatory behavior of damped second-order nonlinear delay differential equations with riemann-stieltjes integral." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017693.

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