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Journal articles on the topic 'Kurzweil-Henstock integral'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Tulone, Francesco. "Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space." Tatra Mountains Mathematical Publications 49, no. 1 (December 1, 2011): 81–88. http://dx.doi.org/10.2478/v10127-011-0027-z.

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ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.

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12

Sinay, Lexy J. "SIFAT-SIFAT DASAR INTEGRAL HENSTOCK." BAREKENG: Jurnal Ilmu Matematika dan Terapan 6, no. 2 (December 1, 2012): 7–15. http://dx.doi.org/10.30598/barekengvol6iss2pp7-15.

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This paper was a review about theory of Henstock integral. Riemann gave a definition of integral based on the sum of the partitions in Integration area (interval [a, b]). Thosepartitions is a  -positive constant. Independently, Henstock and Kurzweil replaces - positive constant on construction Riemann integral into a positive function, ie (x)>0 forevery x[a, b]. This function is a partition in interval [a, b]. From this partitions, we can defined a new integral called Henstock integral. Henstock integral is referred to as acomplete Riemann integral, because the basic properties of the Henstock integral is more constructive than Riemann Integral.

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13

Malý, Jan, and Washek F. Pfeffer. "Henstock-Kurzweil integral on $BV$ sets." Mathematica Bohemica 141, no. 2 (May 20, 2016): 217–37. http://dx.doi.org/10.21136/mb.2016.16.

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14

Di Piazza, L., and K. MusiaŁ. "Set-Valued Kurzweil–Henstock–Pettis Integral." Set-Valued Analysis 13, no. 2 (June 2005): 167–79. http://dx.doi.org/10.1007/s11228-004-0934-0.

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15

Tulone, Francesco. "Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms." Tatra Mountains Mathematical Publications 42, no. 1 (December 1, 2009): 27–37. http://dx.doi.org/10.2478/v10127-009-0003-z.

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Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

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16

Satco, Bianca. "Volterra integral inclusions via Henstock-Kurzweil-Pettis integral." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 26, no. 1 (2006): 87. http://dx.doi.org/10.7151/dmdico.1066.

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17

Sikorska-Nowak, Aneta, and Grzegorz Nowak. "Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–14. http://dx.doi.org/10.1155/2007/65947.

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We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

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18

Talvila, Erik. "Estimates of Henstock-Kurzweil Poisson Integrals." Canadian Mathematical Bulletin 48, no. 1 (March 1, 2005): 133–46. http://dx.doi.org/10.4153/cmb-2005-012-8.

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AbstractIf f is a real-valued function on [−π, π] that is Henstock-Kurzweil integrable, let ur(θ) be its Poisson integral. It is shown that ∥ur∥p = o(1/(1 − r)) as r → 1 and this estimate is sharp for 1 ≤ p ≤ ∞. If μ is a finite Borel measure and ur(θ) is its Poisson integral then for each 1 ≤ p ≤ ∞ the estimate ∥ur∥p = O((1−r)1/p−1) as r → 1 is sharp. The Alexiewicz norm estimates ∥ur∥ ≤ ∥f ∥ (0 ≤ r < 1) and ∥ur − f∥ → 0 (r → 1) hold. These estimates lead to two uniqueness theorems for the Dirichlet problem in the unit disc with Henstock-Kurzweil integrable boundary data. There are similar growth estimates when u is in the harmonic Hardy space associated with the Alexiewicz norm and when f is of bounded variation.

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19

Yang, Haifeng, and Tin Lam Toh. "On Henstock-Kurzweil method to Stratonovich integral." Mathematica Bohemica 141, no. 2 (May 20, 2016): 129–42. http://dx.doi.org/10.21136/mb.2016.11.

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20

Congxin, Wu, Li Baolin, and E. Stanley Lee. "Discontinuous Systems and the Henstock–Kurzweil Integral." Journal of Mathematical Analysis and Applications 229, no. 1 (January 1999): 119–36. http://dx.doi.org/10.1006/jmaa.1998.6149.

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21

Ye, Guoju, and Wei Liu. "The distributional Henstock–Kurzweil integral and applications." Monatshefte für Mathematik 181, no. 4 (December 14, 2015): 975–89. http://dx.doi.org/10.1007/s00605-015-0853-1.

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22

Heikkilä, S. "Differential and integral equations with Henstock–Kurzweil integrable functions." Journal of Mathematical Analysis and Applications 379, no. 1 (July 2011): 171–79. http://dx.doi.org/10.1016/j.jmaa.2010.12.050.

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23

Zhou, Dakai, Guoju Ye, Wei Liu, and Bing Liang. "The Application of Distributional Henstock-Kurzweil Integral on Third-order Three-Point Nonlinear Boundary-Value Problems." Journal of Mathematics Research 7, no. 4 (November 24, 2015): 150. http://dx.doi.org/10.5539/jmr.v7n4p150.

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We consider a type of form such as $u'''=-f$ with three-point<br />nonlinear boundary-value problems (NBVPs). We verified the existence<br />of solutions of the (NBVPs) when $f$ is distributional<br />Henstock-Kurzweil integral but not Henstock-Kurzweil integral.We use<br />the distribution derivative and fixed point theorem to deal with the<br />problem. The results obtained generalize the known results. For<br />this reason, it is conducive to the further study of NBVPS.

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24

Tulone, Francesco. "Inversion formulae for the integral transform on a locally compact zero-dimensional group." Tatra Mountains Mathematical Publications 44, no. 1 (December 1, 2009): 53–63. http://dx.doi.org/10.2478/v10127-009-0047-0.

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Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.

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25

Bianconi, Ricardo, João C. Prandini, and Cláudio Possani. "A Daniell integral approach to nonstandard Kurzweil-Henstock integral." Czechoslovak Mathematical Journal 49, no. 4 (December 1999): 817–23. http://dx.doi.org/10.1023/a:1022457218754.

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26

Boccuto, A., D. Candeloro, and A. R. Sambucini. "A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral." Journal of Function Spaces and Applications 9, no. 3 (2011): 283–304. http://dx.doi.org/10.1155/2011/158412.

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27

Coghetto, Roland. "Gauge Integral." Formalized Mathematics 25, no. 3 (October 1, 2017): 217–25. http://dx.doi.org/10.1515/forma-2017-0021.

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Summary Some authors have formalized the integral in the Mizar Mathematical Library (MML). The first article in a series on the Darboux/Riemann integral was written by Noboru Endou and Artur Korniłowicz: [6]. The Lebesgue integral was formalized a little later [13] and recently the integral of Riemann-Stieltjes was introduced in the MML by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama [12]. A presentation of definitions of integrals in other proof assistants or proof checkers (ACL2, COQ, Isabelle/HOL, HOL4, HOL Light, PVS, ProofPower) may be found in [10] and [4]. Using the Mizar system [1], we define the Gauge integral (Henstock-Kurzweil) of a real-valued function on a real interval [a, b] (see [2], [3], [15], [14], [11]). In the next section we formalize that the Henstock-Kurzweil integral is linear. In the last section, we verified that a real-valued bounded integrable (in sense Darboux/Riemann [6, 7, 8]) function over a interval a, b is Gauge integrable. Note that, in accordance with the possibilities of the MML [9], we reuse a large part of demonstrations already present in another article. Instead of rewriting the proof already contained in [7] (MML Version: 5.42.1290), we slightly modified this article in order to use directly the expected results.

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28

Mei, Hui, Guoju Ye, Wei Liu, and Yanrong Chen. "Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral." Journal of Mathematics Research 9, no. 5 (September 5, 2017): 46. http://dx.doi.org/10.5539/jmr.v9n5p46.

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In this paper, we apply the method associated with the technique of measure of noncompactness and some generalizations of Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile, an example is provided to illustrate our results.

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29

Sworowski, Piotr. "Some Kurzweil-Henstock-type integrals and the wide Denjoy integral." Czechoslovak Mathematical Journal 57, no. 1 (March 2007): 419–34. http://dx.doi.org/10.1007/s10587-007-0070-8.

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30

Leader. "Basic Convergence Principles for the Kurzweil-Henstock Integral." Real Analysis Exchange 18, no. 1 (1992): 95. http://dx.doi.org/10.2307/44133049.

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31

Liu, Wei, Guoju Ye, and Dafang Zhao. "The distributional Henstock-Kurzweil integral and applications II." Journal of Nonlinear Sciences and Applications 10, no. 1 (January 29, 2017): 290–98. http://dx.doi.org/10.22436/jnsa.010.01.27.

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32

Wibowo, Ratno Bagus Edy, and Mohamad Muslikh. "The Henstock-Kurzweil integral of set-valued function." International Journal of Mathematical Analysis 8 (2014): 2741–55. http://dx.doi.org/10.12988/ijma.2014.410332.

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33

Sokol B. Memetaj. "A Convergence Theorem for the Henstock-Kurzweil Integral." Real Analysis Exchange 35, no. 2 (2010): 509. http://dx.doi.org/10.14321/realanalexch.35.2.0509.

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34

Antoine JULIA. "A Henstock-Kurzweil type integral on one dimensional integral currents." Bulletin de la Société mathématique de France 148, no. 2 (2020): 283–319. http://dx.doi.org/10.24033/bsmf.2806.

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35

Kawasaki, Toshiharu. "Denjoy integral and Henstock-Kurzweil integral in vector lattices, I." Czechoslovak Mathematical Journal 59, no. 2 (June 2009): 381–99. http://dx.doi.org/10.1007/s10587-009-0027-1.

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36

Kawasaki, Toshiharu. "Denjoy integral and Henstock-Kurzweil integral in vector lattices, II." Czechoslovak Mathematical Journal 59, no. 2 (June 2009): 401–17. http://dx.doi.org/10.1007/s10587-009-0028-0.

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37

Gou, Haide, and Yongxiang Li. "Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 2 (April 26, 2020): 135–45. http://dx.doi.org/10.1515/ijnsns-2018-0174.

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AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

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38

Lu, Yueping, Guoju Ye, Ying Wang, and Wei Liu. "The Darboux problem involving the distributional Henstock–Kurzweil integral." Proceedings of the Edinburgh Mathematical Society 55, no. 1 (January 4, 2012): 197–205. http://dx.doi.org/10.1017/s0013091510001343.

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AbstractIn this paper, using the Schauder Fixed Point Theorem and the Vidossich Theorem, we study the existence of solutions and the structure of the set of solutions of the Darboux problem involving the distributional Henstock–Kurzweil integral. The two theorems presented in this paper are extensions of the previous results of Deblasi and Myjak and of Bugajewski and Szufla.

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39

Wang, Hongmei, Guoju Ye, Hao Zhou, and Bing Liang. "A Method to Construct Sets of Commuting Matrices." Journal of Mathematics Research 7, no. 2 (May 23, 2015): 195. http://dx.doi.org/10.5539/jmr.v7n2p195.

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Using the method of upper and lower solutions, we study theexistence of solutions of the hyperbolic equation involving thedistributional Henstock-Kurzweil integral. Results presented in thispaper are extension of the previous results in the literatures.

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40

Skvortsov, Valentin, and Francesco Tulone. "Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space." gmj 16, no. 3 (September 2009): 575–82. http://dx.doi.org/10.1515/gmj.2009.575.

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Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.

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41

Maldeniya, Amila J., Naleen C. Ganegoda, Kaushika De Silva, and Sanath K. Boralugoda. "Solving Poisson Equation by Distributional HK-Integral: Prospects and Limitations." International Journal of Mathematics and Mathematical Sciences 2021 (July 10, 2021): 1–9. http://dx.doi.org/10.1155/2021/5511283.

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In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function D ℝ 2 . Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson’s equation in the upper half space ℝ + 3 with Dirichlet boundary condition.

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42

BONGIORNO, DONATELLA, and GIUSEPPA CORRAO. "ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS." Fractals 23, no. 02 (May 28, 2015): 1550008. http://dx.doi.org/10.1142/s0218348x15500085.

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The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

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43

Alewine, J. Alan, Eric Schechter, Lee Peng Yee, and Rudolf Vyborny. "The Integral: An Easy Approach after Kurzweil and Henstock." American Mathematical Monthly 108, no. 6 (June 2001): 577. http://dx.doi.org/10.2307/2695730.

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44

Liu, G. Ye and W. "The Distributional Henstock-Kurzweil Integral and Applications: a Survey." Journal of Mathematical Study 49, no. 4 (June 2016): 433–48. http://dx.doi.org/10.4208/jms.v49n4.16.06.

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45

TUO–YEONG, LEE. "A characterisation of multipliers for the Henstock–Kurzweil integral." Mathematical Proceedings of the Cambridge Philosophical Society 138, no. 3 (May 2005): 487–92. http://dx.doi.org/10.1017/s030500410500839x.

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46

ŠTAJNER-PAPUGA, IVANA. "HENSTOCK–KURZWEIL TYPE INTEGRAL BASED ON GENERALIZED g-SEMIRING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, supp01 (December 2002): 89–104. http://dx.doi.org/10.1142/s0218488502001855.

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We shall consider special class of generalized semiring based on generalized pseudo-operations of the following form: x ⊕ y = g(-1)(εg(x) + g(y)), x ⊙ y = g(-1)(g(x)γg(y)), where ε and γ are arbitrary but fixed positive real numbers, g is a positive strictly monotone generating function and g(-1) is its pseudo-inverse. Using this pseudo-operations, corresponding pseudo-measure and the Henstock–Kurzweil type integral will be introduced and investigated.

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47

Mema, Esterina. "Equiintegrability and controlled convergence for the Henstock-Kurzweil integral." International Mathematical Forum 8 (2013): 913–19. http://dx.doi.org/10.12988/imf.2013.13097.

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48

Ben Amar, Afif. "On an integral equation under Henstock–Kurzweil–Pettis integrability." Arabian Journal of Mathematics 4, no. 2 (January 10, 2015): 91–99. http://dx.doi.org/10.1007/s40065-014-0125-2.

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49

Skvortsov, Valentin, and Francesco Tulone. "Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group." Tatra Mountains Mathematical Publications 44, no. 1 (December 1, 2009): 41–51. http://dx.doi.org/10.2478/v10127-009-0046-1.

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Abstract:

Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.

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50

Lone, Nisar A., and T. A. Chishti. "Fundamental theorem of calculus under weaker forms of primitive." Acta Universitatis Sapientiae, Mathematica 10, no. 1 (August 1, 2018): 101–11. http://dx.doi.org/10.2478/ausm-2018-0009.

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Abstract:

Abstract In this paper we will present abstract versions of fundamental theorem of calculus (FTC) in the setting of Kurzweil - Henstock integral for functions taking values in an infinite dimensional locally convex space. The result will also be dealt with weaker forms of primitives in a widespread setting of integration theories generalising Riemann integral.

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