Two Types of Multilinear Stieltjes Integrals in the Henstock-Kurzweil Sense

Authors

  • Armin Halilović The Royal Institute of Technology, KTH STH, Campus Haninge, Haninge, Sweden

DOI:

https://doi.org/10.5644/SJM.05.1.03

Keywords:

Multilinear integral, Stieltjes integral, Henstock-Kurzweil integral, Moore-Pollard-Stieltjes integral

Abstract

In this paper we examine and compare two types of multilinear integrals considering their Stieltjes sums. The convergence of the Stieltjes sums is considered in the Riemann, Moore-Pollard and Henstock-Kurzweil sense.

 

2000 Mathematics Subject Classification. 28B05, 46G12

Downloads

Download data is not yet available.

References

A. Halilovi´c, Multilinear Stieltjes integrals in Banach spaces, Rad. Mat., 7 (1991), 305–316.

A. Halilovi´c, Calculus for the multilinear Stieltjes integral, Glas. Mat., III. Ser., 27(47) (1992), 227–240.

A. Halilovi´c, On some properties of bilinear and multilinear Stieltjes integrals, Rad. Mat., 8 (1992/98), 201–215.

A. Halilovi´c, Semi-variation and multilinear Stieltjes integrals, Glas. Mat., III. Ser., 32(52) (1997), 17–28.

A. Halilovi´c, Oscillation and multilinear Stieltjes integrals, Glas. Mat., III. Ser., 36(56) (2001), 17–31.

R. Henstock, The General Theory of Integration, Clarendon Press, Oxford, 1991.

T. H. Hildebrandt, Introduction to the Theory of Integration, Academic press, New York-London, 1963.

T. H. Hildebrandt, On systems of linear differentio-Stieltjes-integral equations, Illinois J. Math., 3 (1959), 352–373.

P. Y. Lee, Lanzhou Lectures on Henstock Integration, Word Scientific Publ.Co., Singapore-New Jersey-London-Hong Kong, 1989.

P. Y. Lee, R. V´yborn´y, Integral: an easy approach after Kurzweil and Henstock, Australian Mathematical Society Lecture Series, 14. Cambridge University Press, Cambridge, 2000.

J. S. Mac Nerney, Stieltjes integral in linear spaces, Ann. Math., 61 (1955), 354–367.

F. P. Jamil, S. R. Canoy, The trilinear Henstock integral $int_a^b A(f,g,dh)$ in Banach spaces, Matimyas Mat., 24 (2001), 1–13.

Downloads

Published

11.06.2024

How to Cite

Halilović, A. (2024). Two Types of Multilinear Stieltjes Integrals in the Henstock-Kurzweil Sense. Sarajevo Journal of Mathematics, 5(1), 21–39. https://doi.org/10.5644/SJM.05.1.03

Issue

Section

Articles