Study of Henstock-Kurzweil integrals

Khinal Parmar

doi:https://doi.org/10.14445/22315373/IJMTT-V19P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 19 | Number 2 | Year 2015 | Article Id. IJMTT-V19P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P517

Study of Henstock-Kurzweil integrals

Khinal Parmar

Citation :

Khinal Parmar, "Study of Henstock-Kurzweil integrals," International Journal of Mathematics Trends and Technology (IJMTT), vol. 19, no. 2, pp. 130-135, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V19P517

Abstract

In this paper a brief introduction to Henstock-Kurzweil integrals is given based on previous studies. This paper explains about definition and some properties of Henstock-Kurzweil integral. Henstock-Kurzweil integral is generalized from Riemann integral. The theory of the Riemann integral was not fully satisfactory. Many important functions do not have Riemann integral. So, Henstock and Kurzweil made the new theory of integral.

Keywords

gauge, "δ" - fine partition, Henstock-Kurzweil integral

References

[1] Gordon R.,Real Analysis: A First Course, 2nd edition, Addison-Wesley Higher Mathematics.
[2] Katz V.,A History of Mathematics: An Introduction, 3rd edition, Addison-Wesley Higher Mathematics.
[3] Lee Tuo Yeong,Henstock-Kurzweil Integration on Euclidean Spaces, World Scientific Publishing Co Pte Ltd.
[4] Bartle R. G. and Sherbert D.,Introduction to Real Analysis - Third edition, John Wiley and Sons, New York.
[5] Lang Searge,Analysis I, Addison-Wesley Publishing Company, New York.
[6] Lee Peng Yee,Lanzhou Lectures on Henstock Integration, World Scientific Publishing Co Pte Ltd.
[7] Lee Peng Yee and Rudolf Výborný,Integral: An easy approach after Kurzweil and Henstock, Cambridge University Press.
[8] Ma Zheng Min and Lee Peng Yee, An overview of classical integration theory
[9] Anil Pedgaonkar, Fundamental theorem of calculus for Henstock -Kurzweil integral, Bulletin of the Marathwada Mathematical Society Vol. 14, No. 1, June 2013, Pages 71-80.
[10] Jonathan Wells, Generalizations of the Riemann Integral: An Investigation of the Henstock Integral