International Journal of Nonlinear Analysis and Applications
On ap-sequential Henstock integral for interval valued functions
Document Type : Research Paper
Authors
Department of Mathematics, University of Lagos, Lagos, Nigeria
Abstract
The aim of this paper is to introduce the notion of interval ap-Sequential Henstock integral(shortly, the ap-ISH . Some interesting properties of ap-ISH are investigated.
Keywords
[1] M.E. Hamid, L. Xu and Z. Gong, The Henstock-Stieltjes integral for set valued fFunctions, Int. J. Pure Appl.
Math. 114 (2017), no. 2, 261–275.
[2] M.E. Hamid, A.H. Elmuiz and M.E. Sheima, On AP-Henstock integral interval Of valued functions and fuzzyvalued functions, J. Appl. Math. 7 (2016), no. 18, 2285–2295.
[3] R. Henstock, The general theory of integration. Oxford University Press, Oxford, UK, 1991.
[4] O. Holzmann, B. Lang and H. Schutt, Newton’s constant of gravitation and verified numerical quadratures, Reliable
Comput. 2 (1996), no. 3, 229–240.
[5] V.O. Iluebe and A.A. Mogbademu, Dominated and bounded convergence results of sequential Henstock Stieltjes
integral in real valued space, J. Nepal Math. Soc. 3 (2020), no. 1, 17–20.
[6] V.O. Iluebe and A.A. Mogbademu, Equivalence Of Henstock and certain sequential Henstock integral, Bangmond
Int. J. Math. Comput. Sci. 1 (2020), no. 1-2, 9–16.
[7] W. Kramer and S. Wedner, Two adaptive Gauss-Legendre type algorithms for the verified computation of definite
integrals, Reliable Comput. 2 (1996), no. 3, 241–254.
[8] B. Lang, Derivative-based subdivision in multi-dimensional verified Gaussian quadrature, Symbolic algebraic methods and verification methods. Springer, Vienna, 2001, pp. 145–152.
[9] L.A. Paxton, Sequential approach to the Henstock integral, Washington State University, arXiv:1609.05454v1
[maths.CA], 2016.
[10] R.E. Moore, R.B. Kearfott and M.J. Cloud, Introduction to iInterval analysis, Society for Industrial and Applied
Mathematics, 2009.[11] E. van Dijk, The Henstock-Kurzweil integral., Bachelorthesis Mathematics, Rijkuniversiteit Groningen, 2014.
[12] C.X. Wu and Z.T. Gong, On Henstock integrals of interval-valued functions and fuzzy-valued functions, Fuzzy
Sets Syst. 115 (2000), no. 3, 377–391.
Math. 114 (2017), no. 2, 261–275.
[2] M.E. Hamid, A.H. Elmuiz and M.E. Sheima, On AP-Henstock integral interval Of valued functions and fuzzyvalued functions, J. Appl. Math. 7 (2016), no. 18, 2285–2295.
[3] R. Henstock, The general theory of integration. Oxford University Press, Oxford, UK, 1991.
[4] O. Holzmann, B. Lang and H. Schutt, Newton’s constant of gravitation and verified numerical quadratures, Reliable
Comput. 2 (1996), no. 3, 229–240.
[5] V.O. Iluebe and A.A. Mogbademu, Dominated and bounded convergence results of sequential Henstock Stieltjes
integral in real valued space, J. Nepal Math. Soc. 3 (2020), no. 1, 17–20.
[6] V.O. Iluebe and A.A. Mogbademu, Equivalence Of Henstock and certain sequential Henstock integral, Bangmond
Int. J. Math. Comput. Sci. 1 (2020), no. 1-2, 9–16.
[7] W. Kramer and S. Wedner, Two adaptive Gauss-Legendre type algorithms for the verified computation of definite
integrals, Reliable Comput. 2 (1996), no. 3, 241–254.
[8] B. Lang, Derivative-based subdivision in multi-dimensional verified Gaussian quadrature, Symbolic algebraic methods and verification methods. Springer, Vienna, 2001, pp. 145–152.
[9] L.A. Paxton, Sequential approach to the Henstock integral, Washington State University, arXiv:1609.05454v1
[maths.CA], 2016.
[10] R.E. Moore, R.B. Kearfott and M.J. Cloud, Introduction to iInterval analysis, Society for Industrial and Applied
Mathematics, 2009.[11] E. van Dijk, The Henstock-Kurzweil integral., Bachelorthesis Mathematics, Rijkuniversiteit Groningen, 2014.
[12] C.X. Wu and Z.T. Gong, On Henstock integrals of interval-valued functions and fuzzy-valued functions, Fuzzy
Sets Syst. 115 (2000), no. 3, 377–391.
)
Volume 13, Issue 2
July 2022Pages 3095-3103
- Receive Date: 04 November 2021
- Revise Date: 10 December 2021
- Accept Date: 15 December 2021