Relevant bibliographies by topics / Kurzweil-Henstock integral

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Kurzweil-Henstock integral'

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Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Kurzweil-Henstock integral"

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Afiyah, Siti Nurul. "Henstock-Kurzweil Integral on [a,b]." CAUCHY 2, no. 1 (November 18, 2011): 24. http://dx.doi.org/10.18860/ca.v2i1.1805.

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<div class="standard"><a id="magicparlabel-2402">The theory of the Riemann integral was not fully satisfactory. Many important functions do not have a Riemann integral. So, Henstock and Kurzweil make the new theory of integral. From the background, the writer will be research about Henstock-Kurzweil integral and also theorems of Henstock- Kurzweil Integral. Henstock- Kurzweil Integral is generalized from Riemann integral. In this case the writer uses research methods literature or literature study carried out by way explore, observe, examine and identify the existing knowledge in the literature. In this thesis explain about partition which used in Henstock- Kurzweil Integral, definition and some property of Henstock- Kurzweil Integral. And some properties of Henstock- Kurzweil integral as follows: value of the Henstock- Kurzweil integral is unique, linearity of the Henstock-Kurzweil integral, Additivity of the Henstock-Kurzweil integral, Cauchy criteria, nonnegativity of Henstock-Kurzweil integral and primitive function.</a></div>
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LIU, WEI, GUOJU YE, YING WANG, and XUEYUAN ZHOU. "ON PERIODIC SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS INVOLVING THE DISTRIBUTIONAL HENSTOCK–KURZWEIL INTEGRAL." Bulletin of the Australian Mathematical Society 86, no. 2 (February 6, 2012): 327–38. http://dx.doi.org/10.1017/s0004972711003455.

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AbstractThe purpose of this paper is to study the existence of periodic solutions and the topological structure of the solution set of first-order differential equations involving the distributional Henstock–Kurzweil integral. The distributional Henstock–Kurzweil integral is a general integral, which includes the Lebesgue and Henstock–Kurzweil integrals. The main results extend some previously known results in the literature.
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Sánchez-Perales, Salvador, Francisco J. Mendoza Torres, and Juan A. Escamilla Reyna. "Henstock-Kurzweil Integral Transforms." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/209462.

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Cunanan, Andrew Felix IV Suarez, and Julius Benitez. "Simple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions." European Journal of Pure and Applied Mathematics 13, no. 1 (January 31, 2020): 130–43. http://dx.doi.org/10.29020/nybg.ejpam.v13i1.3626.

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Henstock--Kurzweil integral, a nonabsolute integral, is a natural extension of the Riemann integral that was studied independently by Ralph Henstock and Jaroslav Kurzweil. This paper will introduce the Henstock--Kurzweil--Stieltjes integral of $\mathcal{C}[a,b]$-valued functions defined on a closed interval $[f,g]\subseteq\mathcal{C}[a,b]$, where $\mathcal{C}[a,b]$ is the space of all continuous real-valued functions defined on $[a,b]\subseteq\mathbb{R}$. Some simple properties of this integral will be formulated including the Cauchy criterion and an existence theorem will be provided.
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Cunanan, Andrew Felix IV Suarez, and Julius Benitez. "Simple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions." European Journal of Pure and Applied Mathematics 13, no. 1 (January 31, 2020): 130–43. http://dx.doi.org/10.29020/nybg.ejpam.v1i1.3626.

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Henstock--Kurzweil integral, a nonabsolute integral, is a natural extension of the Riemann integral that was studied independently by Ralph Henstock and Jaroslav Kurzweil. This paper will introduce the Henstock--Kurzweil--Stieltjes integral of $\mathcal{C}[a,b]$-valued functions defined on a closed interval $[f,g]\subseteq\mathcal{C}[a,b]$, where $\mathcal{C}[a,b]$ is the space of all continuous real-valued functions defined on $[a,b]\subseteq\mathbb{R}$. Some simple properties of this integral will be formulated including the Cauchy criterion and an existence theorem will be provided.
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Borkowski, Marcin, and Daria Bugajewska. "Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations." Mathematica Slovaca 68, no. 1 (February 23, 2018): 77–88. http://dx.doi.org/10.1515/ms-2017-0082.

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Abstract In this paper we are going to apply the Henstock-Kurzweil integrals defined on an unbounded intervals to differential and integral equations defined on such intervals. To deal with linear differential equations we examine convolution involving functions integrable in Henstock-Kurzweil sense. In the case of nonlinear Hammerstein integral equation as well as Volterra integral equation we look for solutions in the space of functions of bounded variation in the sense of Jordan.
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LIU, WEI, GUOJU YE, and DAFANG ZHAO. "Multiple existence of solutions for a coupled system involving the distributional Henstock-Kurzweil integral." Carpathian Journal of Mathematics 34, no. 1 (2018): 77–84. http://dx.doi.org/10.37193/cjm.2018.01.08.

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This paper deals with a coupled system in the sense of distributions (generalized functions). Our main goal is to get the basic multiple existence results via some degree theory arguments. Differently from the literatures, the proof is based on the concept of a general integral named distributional Henstock-Kurzweil integral, which includes the Lebesgue and Henstock-Kurzweil integrals as special cases. Finally, an example is given to illustrate that the presented abstract theory contains some previous results as special cases.
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BONGIORNO, B., L. DI PIAZZA, and K. MUSIAŁ. "APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS." Glasgow Mathematical Journal 50, no. 3 (September 2008): 583–93. http://dx.doi.org/10.1017/s0017089508004448.

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AbstractThe approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.
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Racca, Abraham Perral, and Emmanuel A. Cabral. "The N-Integral." Journal of the Indonesian Mathematical Society 26, no. 2 (July 10, 2020): 242–57. http://dx.doi.org/10.22342/jims.26.2.865.242-257.

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In this paper, we introduced a Henstock-type integral named N-integral of a real valued function f on a closed and bounded interval [a,b]. The set N-integrable functions lie entirely between Riemann integrable functions and Henstock-Kurzweil integrable functions. Furthermore, this new integral integrates all improper Riemann integrable functions even if they are not Lebesgue integrable. It was shown that for a Henstock-Kurzweil integrable function f on [a,b], the following are equivalent:The function f is N-integrable;There exists a null set S for which given epsilon 0 there exists a gauge delta such that for any delta-fine partial division D={(xi,[u,v])} of [a,b] we have [(phi_S(D) Gamma_epsilon) sum |f(v)-f(u)||v-u|epsilon] where phi_S(D)={(xi,[u,v])in D:xi not in S} and [Gamma_epsilon={(xi,[u,v]): |f(v)-f(u)|= epsilon}] andThe function f is continuous almost everywhere. A characterization of continuous almost everywhere functions was also given.
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Sikorska-Nowak, Aneta. "Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals." Abstract and Applied Analysis 2010 (2010): 1–17. http://dx.doi.org/10.1155/2010/836347.

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We prove existence theorems for integro-differential equations , , , , where denotes a time scale (nonempty closed subset of real numbers ), and is a time scale interval. The functions are weakly-weakly sequentially continuous with values in a Banach space , and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral. This integral generalizes the Henstock-Kurzweil delta integral and the Pettis integral. Additionally, the functions and satisfy some boundary conditions and conditions expressed in terms of measures of weak noncompactness. Moreover, we prove Ambrosetti's lemma.
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Dissertations / Theses on the topic "Kurzweil-Henstock integral"

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David, Manolis. "The Henstock–Kurzweil Integral." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-166430.

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Since the introduction of the Riemann integral in the middle of the nineteenth century, integration theory has been subject to significant breakthroughs on a relatively frequent basis. We have now reached a point where integration theory has been thoroughly researched to a point where one has to delve quite deep into a particular subject in order to encounter open conjectures. In education the Riemann integral has for quite some time been the standard integral in elementary analysis courses and as the complexity of these courses incrementally increase the more general Lebesgue integral eventually becomes the standard integral.  Unfortunately, in the transition from the Riemann integral to the Lebesgue integral there are certain topics of pure theoretical interest which to a certain extent are neglected. This is particularly the case for topics regarding the inverse relationship between differential and integral calculus and the integration of exceedingly complicated functions which for example might be of a highly oscillatory nature. From an applied mathematician's point of view, the partial neglection of these topics in the case of highly problematic functions might be justified in the sense that this theory is unnecessary for modeling most problems that appear in nature. From a theoretician's point of view however this negligence is unacceptable. Consequently, there are alternative integrals which give rise to theories which one can use in an attempt to study these aforementioned topics. An example of such an integral is the Henstock–Kurzweil integral, which can be developed in a rather similar manner to that of the Riemann integral.  In this thesis we will develop the Henstock–Kurzweil integral in order to answer some of the questions which to a certain extent are beyond the scope of the Lebesgue integral while using rather basic proof techniques from complex analysis and measure theory. In addition to that we extended various properties of the Lebesgue integral to the Henstock–Kurzweil integral, in particular when it comes to Lebesgue's fundamental theorem of calculus and the basic convergence theorems of the Lebesgue integral.
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McInnis, Erik O. "Gauge integration." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2002. http://library.nps.navy.mil/uhtbin/hyperion-image/02%5FMcInnis.pdf.

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Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, September 2002.
Thesis advisor(s): Chris Frenzen, Bard Mansager. Includes bibliographical references (p. 49). Also available online.
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Marques, Rafael dos Santos. "Integral equations in the sense of Kurzweil integral and applications." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08112016-104931/.

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Being part of a research group on functional differential equations (FDEs, for short), due to my formation in non-absolute integration theory and because certain kinds of FDEs can be expressed as integral equations, I was motivated to investigate the latter. The purpose of this work, therefore, is to develop the theory of integral equations, when the integrals involved are in the sense of Kurzweil- Henstock or Kurzweil-Henstock-Stieltjes, through the correspondence between solutions of integral equations and solutions of generalized ordinary differential equations (we write generalized ODEs, for short). In order to be able to obtain results for integral equations, we propose extensions of both the Kurzweil integral and the generalized ODEs (found in [36]). We develop the fundamental properties of this new generalized ODE, such as existence and uniqueness of solutions results, and we propose stability concepts for the solutions of our new class of equations. We, then, apply these results to a class of nonlinear Volterra integral equations of the second kind. Finally, we consider a model of population growth (found in [4]) that can be expressed as an integral equation that belongs to this class of nonlinear Volterra integral equations.
Sendo parte de um grupo de pesquisa em equações diferenciais funcionais (escrevemos EDFs), por causa de minha formação em teoria de integração não absoluta e porque certos tipos de EDFs podem ser escritas como equações integrais, decidi estudar esse último tipo de equações. O objetivo desse trabalho, portanto, é desenvolver a teoria de equações integrais, quando as integrais envolvidas são no sentido de Kurzweil-Henstock ou Kurzweil-Henstock-Stieltjes, através da correspondência entre soluções de equações integrais e soluções de equações diferenciais ordinárias generalizadas (ou EDOs generalizadas). A fim de obter resultados para estas equações integrais, propomos extensões de ambas a integral de Kurzweil e as EDOs generalizadas (encontradas em [36]). Desenvolvemos propriedades fundamentais dessa nova EDO generalizada, como resultados de existência e unicidade de solução, e propomos conceitos de estabilidade para as soluções de nossa nova classe de equações. Nós, então, aplicamos esses resultados a uma classe de equações integrais de Volterra não lineares de segunda espécie. Finalmente, consideramos um modelo de crescimento de populações (encontrado em [4]) que pode ser escrito como uma equação integral pertencente a essa classe de equações integrais de Volterra não lineares.
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Hoffmann, Heiko [Verfasser], and R. [Akademischer Betreuer] Schnaubelt. "Descriptive characterisation of the variational Henstock-Kurzweil-Stieltjes integral and applications / Heiko Hoffmann. Betreuer: R. Schnaubelt." Karlsruhe : KIT-Bibliothek, 2014. http://d-nb.info/1069324043/34.

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Bastian, Ryan. "An Introduction to the Generalized Riemann Integral and Its Role in Undergraduate Mathematics Education." Ashland University Honors Theses / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1482504144122774.

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Acuña, Rogelio Grau. "On qualitative properties of generalized ODEs." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-26102016-090644/.

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In this work, our goal is to prove results on prolongation of solutions, uniform boundedness of solutions, uniform stability as well uniform asymptotic stability (in the classical sense of Lyapunov) for measure differential equations and for dynamic equations on time scales. In order to get our results, we employ the theory of generalized ODEs, since these equations encompass measure differential equations and dynamic equations on time scales. Therefore, to get our results, we start by proving the expected result for abstract generalized ODEs. Then, using the correspondence between the solutions of these equations and the solutions of measure differential equations (see [38]), we extend all the results to these the latter. After that, using the correspondence between the solutions of measure differential equations and the solutions of dynamic equations on time scales (see [21]), we extend all the results to these last equations. Finally, we investigate autonomous generalized ODEs and show that these equations do not enlarge the class of classical autonomous ODEs, even when we consider a more general class of functions as right-hand sides. All the new results presented in this work are contained in papers [16, 17, 18, 19].
Neste trabalho, nosso objetivo e provar resultados sobre prolongamento de soluções, limitação uniforme de soluções, estabilidade uniforme e estabilidade uniforme assintótica (no sentido clássico de Lyapunov) para equações diferenciais em medida e para equações dinâmicas em escalas temporais. A fim de obter os nossos resultados, empregamos a teoria de EDOs generalizadas, uma vez que estas equações abrangem equações diferenciais em medida e equações dinâmicas em escalas temporais. Portanto, para obter nossos resultados, vamos começar por provar, os resultados que queremos para EDOs generalizadas abstratas. Em seguida, usando a correspondência entre as soluções de EDOs generalizadas e soluções de equações diferenciais em medida (ver [38]), estenderemos os resultados para estas ultimas equações. Depois disso, usando a correspondência entre as soluções de equações diferenciais em medida e as soluções de equações dinâmicas em escalas temporais (ver [21]), estenderemos todos os resultados para estas ultimas equações. Finalmente, investigamos EDOs generalizadas autônomas e mostramos que estas equações não aumentam a classe de EDOs autônomas clássicas, mesmo quando consideramos uma classe mais geral de funções nos lados direitos das equações. Os novos resultados encontrados estão contidos em [16, 17, 18, 19].
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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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Skovajsa, Břetislav. "Zobecněné obyčejné diferenciální rovnice v metrických prostorech." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340897.

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The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.
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Zage, Esmael António. "Derivadas de Dini." Master's thesis, 2018. http://hdl.handle.net/10400.6/10000.

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Neste trabalho lançámos o desafio de estudar derivadas de Dini, o porquê do seu aparecimento e algumas aplicações. Para abordarmos este assunto de uma forma coerente foi necessário traçar um caminho no qual tivemos de recordar alguns conceitos lecionados no Ensino Secundário, como por exemplo: sucessões e subsucessões, limite, função contínua, função diferenciável, monotonia e extremos de uma função; assim como os resultados relacionados. Mas foi também necessário introduzir assuntos que vão além do Ensino Secundário, como limite superior e limite inferior, funções semicontínuas. Para aplicar as derivadas de Dini recordamos os Teoremas de Rolle e de Lagrange, para os quais apresentamos uma generalização envolvendo as derivadas de Dini. Tal como em qualquer curso de Cálculo, depois do cálculo diferencial surge a integração, pois isso no Capítulo final consta os conhecidos integrais de Riemann e Lebesgue e a construção do integral de Henstock-Kurzweil.
In this work we launched the challenge of studying derivatives of Dini, the reason for its appearance and some applications. In order to approach this subject in a coherent way, it was necessary to draw a path in which we had to remember some concepts taught in Secondary Education, such as: sequences and subsequences, limit, continuous function, differentiable function, monotony and extremes of a function; as well as related results. But it was also necessary to introduce subjects that go beyond Secondary Education, as upper limit and lower limit, semicontinuous functions. To apply the Dini derivatives we recall the Rolle and Lagrange Theorems, for which we present a generalization involving the Dini derivatives. As in any Calculus course, after the differential calculus arises integration, for this in the final Chapter consists of the well-known integrals of Riemann and Lebesgue and the construction of the Henstock-Kurzweil integral.
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Kuncová, Kristýna. "Neabsolutně konvergentní integrály." Doctoral thesis, 2019. http://www.nusl.cz/ntk/nusl-408083.

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Title: Nonabsolutely convergent integrals Author: Krist'yna Kuncov'a Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Jan Mal'y, DrSc., Department of Mathematical Analysis Abstract: In this thesis we develop the theory of nonabsolutely convergent Hen- stock-Kurzweil type packing integrals in different spaces. In the framework of metric spaces we define the packing integral and the uniformly controlled inte- gral of a function with respect to metric distributions. Applying the theory to the notion of currents we then prove a generalization of the Stokes theorem. In Rn we introduce the packing R and R∗ integrals, which are defined as charges - additive functionals on sets of bounded variation. We provide comparison with miscellaneous types of integrals such as R and R∗ integral in Rn or MCα integral in R. On the real line we then study a scale of integrals based on the so called p-oscillation. We show that our indefinite integrals are a.e. approximately differ- entiable and we give comparison with other nonabsolutely convergent integrals. Keywords: Nonabsolutely convergent integrals, BV sets, Henstock-Kurzweil in- tegral, Divergence theorem, Analysis in metric measure spaces 1
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Books on the topic "Kurzweil-Henstock integral"

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Lee, Tuo Yeong. Henstock-Kurzweil integration on Euclidean spaces. Singapore: World Scientific, 2011.

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Fonda, Alessandro. The Kurzweil-Henstock Integral for Undergraduates. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95321-2.

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The Kurzweil-Henstock integral and its differentials: A unified theory of integration on R and R (superscript n). New York: M. Dekker, 2001.

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Lanzhou lectures on Henstock integration. Singapore: World Scientific, 1989.

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Henstock integration in the plane. Providence, R.I., USA: American Mathematical Society, 1986.

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1928-, Výborný Rudolf, ed. The integral: An easy approach after Kurzweil and Henstock. Cambridge, UK: Cambridge University Press, 2000.

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Integration between the Lebesgue integral and the Henstock-Kurzweil integral: Its relation to local convex vector spaces. Singapore: World Scientific, 2002.

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Jaroslav, Kurzweil, ed. Theories of integration: The integrals of Riemann, Lebesgue, Henstock-Kurzweil, and Mcshane. River Edge, NJ: World Scientific Pub., 2004.

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Jaroslav, Kurzweil, ed. Theories of integration: The integrals of Riemann, Lebesgue, Henstock-Kurzweil, and Mcshane. 2nd ed. New Jersey: World Scientific, 2012.

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Kurtz, Douglas S. Theories of integration: The integrals of Riemann, Lebesgue, Henstock-Kurzweil, and Mcshane. Singapore: World Scientific Pub., 2005.

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Book chapters on the topic "Kurzweil-Henstock integral"

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Zhao, Dafang, Guoju Ye, Wei Liu, and Delfim F. M. Torres. "The Fuzzy Henstock–Kurzweil Delta Integral on Time Scales." In Differential and Difference Equations with Applications, 525–41. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_41.

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Bongiorno, Benedetto. "The Henstock-Kurzweil Integral." In Handbook of Measure Theory, 587–615. Elsevier, 2002. http://dx.doi.org/10.1016/b978-044450263-6/50014-2.

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"The Henstock–Kurzweil Integral." In A Garden of Integrals, 169–204. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.7135/upo9781614442097.009.

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"The multiple Henstock-Kurzweil integral." In Series in Real Analysis, 21–52. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814324595_0002.

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"Improper Integral." In Kurzweil-Henstock Integral in Riesz spaces, edited by Antonio Boccuto, Beloslav Riecan, and Marta Vrabelova, 84–110. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/978160805003110901010084.

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"(SL)-integral." In Kurzweil-Henstock Integral in Riesz spaces, edited by Antonio Boccuto, Beloslav Riecan, and Marta Vrabelova, 134–65. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/978160805003110901010134.

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"The one-dimensional Henstock-Kurzweil integral." In Series in Real Analysis, 1–20. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814324595_0001.

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"Multipliers for the Henstock-Kurzweil integral." In Series in Real Analysis, 169–203. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814324595_0006.

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"Elementary Introduction to Kurzweil-Henstock Integral." In Kurzweil-Henstock Integral in Riesz spaces, edited by Antonio Boccuto, Beloslav Riecan, and Marta Vrabelova, 1–24. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/978160805003110901010001.

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"Kurzweil - Henstock Integral in Topological Spaces." In Kurzweil-Henstock Integral in Riesz spaces, edited by Antonio Boccuto, Beloslav Riecan, and Marta Vrabelova, 62–70. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/978160805003110901010062.

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Conference papers on the topic "Kurzweil-Henstock integral"

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INDRATI, CHRISTIANA RINI, and SOEPARNA DARMAWIJAYA. "The Consequence of Controlled Densed Theorem of Henstock-Kurzweil Integral in n-Dimensional Euclidean Space." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0023.

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