Sequential Henstock integral for  $L^{p}[0,1]$- interval valued functions

Victor Odalochi Iluebe; Mogbademu Adesanmi Alao

doi:10.26637/mjm1002/008

Abstract

In this paper, we introduce the concept of Sequential Henstock integrals for $ L^{p}[0,1]$- interval valued functions and discuss some of their properties.

Keywords:

Sequential Henstock integral, Interval valued functions, guages, right and left endpoints

Mathematics Subject Classification:

28B05, 28B10, 28B15, 46G10

Authors Imprint References Funding Related Articles Downloads

Victor Odalochi Iluebe Faculty of Science, Department of Mathematics, University of Lagos, Lagos, Nigeria. https://orcid.org/0000-0003-3456-9599
Mogbademu Adesanmi Alao Faculty of Science, Department of Mathematics, University of Lagos, Lagos, Nigeria. https://orcid.org/0000-0002-9978-2043

Pages: 178-186
Date Published: 01-04-2022
Vol. 10 No. 02 (2022): Malaya Journal of Matematik (MJM)

F. Abiac and N.J. Kalton, Topics in Banach Space Theory, Springer. (2006), 10-50.

A. Boccuto and A.R. Sambucini, The Henstock-Kurzweil Integral For Functions Defined on Unbounded Interval with Values in Banach Spaces, Acta Mathematica, 7(2004), 3-17

S.S. CAO, The Henstock Integral For Banach Valued Functions, SEA Bull. Math. 1(1992), 16.

R. Gordon, The Integral of Lebesgues, Denjoy, Perron and Henstock. Graduate Studies in Mathematics. Vol. 4. American Mathematical Society. Providence, RI, (1994), 12-30.

M.E. Hamid And A.H. Elmuiz, On Henstock-Stieltjes Integrals of interval-Valued Functions and FuzzyNumber-Valued Functions, Journal of Applied Mathematics and Physics, 4(2016), 779-786.

R. Henstock, The General Theory of Integration, Oxford University Press, Oxford, UK, (1991), 4-20.

V.O. Iluebe and A.A. Mogbademu, Equivalence Of Henstock And Certain Sequential Henstock Integral, Bangmond International Journal of Mathematical and Computational Science, 1 and 2, (2020), $9-16$.

J.M.R. Macalalag and R.N. Paluga, On The Henstock-Stieltjes Integral For $l_p$ Valued Functions, $0

R.E. Moore, R.B. Kearfott And J.C. Michael, Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, (2009), 37-38; 129-135.

L.A. PAxton, Sequential Approach to the Henstock Integral, Washington State University, arXiv:1609.05454v1 [maths.CA],(2016), 9-13.

C.X. Wu And Z.T. Gong, On Henstock Integrals of interval-Valued Functions and Fuzzy-Number-Valued Functions, Fuzzy Set and Systems, 115(2016), 377-391.

J.H. Y OON , On Henstock-Stieltjes Integrals of interval-Valued Functions On Time Scale, Journal of the

Chungcheong Mathematical Society, 29(2016), 109–115.