Mathematics and Statistics Vol. 11(3), pp. 528 - 533
DOI: 10.13189/ms.2023.110308
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Some Convergence Results for the Strong Versions of Order-integrals in Lattice Spaces


Mimoza Shkembi 1,*, Stela Ceno 1, John Shkembi 2
1 Department of Mathematics, University of Elbasan, Albania
2 Department of Electrical Engineering and Computer Science, United States Military Academy, West Point, United States

ABSTRACT

Integration in Riesz spaces has received significant attention in recent papers. The existing body of literature provides comprehensive analyses of the concepts related to order-type integrals for functions that are defined in ordered vector spaces and Banach lattices, as indicated by the studies covered in [3], [4], [5], [7], [8], [9], and [10]. In our work on strongly order-McShane (Henstock-Kurzweil) equiintegration, we have drawn upon the earlier works of Candeloro and Sambucini [6], as well as Boccuto et al. [1-2], who have conducted investigations in the field of order-type integrals. We have expanded upon their research to develop our own findings. This paper focuses on studying the (o)-McShane integral in ordered spaces, where we emphasize the important fact that investigating the (o)-McShane integral is essential in addition to the (o)-Henstock integral. We highlight that the (o)-McShane integration in Banach lattices has richer properties and is more convenient compared to the (o)-Henstock integral. The properties of (o)-convergence exhibited by ordered McShane integrals are prominently featured in our study. By using (o)-convergence, we have obtained valuable results related to the (o)-McShane integral. We arrive at the same results in Banach lattices as on McShane (Henstock-Kurzweil) norm-integrals, and we demonstrate that the (o)-McShane integral opens up a wide field of study where similar results with Henstock integration can be obtained. The outcomes demonstrate the benefits of utilizing this integration technique in ordered spaces, with potentially significant implications for diverse areas of mathematics and related fields.

KEYWORDS
Banach Lattice, Strongly Order-McShane (Henstock-Kurzweil) Integration, Strongly Order-McShane (Henstock-Kurzweil) Equi-integration

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mimoza Shkembi , Stela Ceno , John Shkembi , "Some Convergence Results for the Strong Versions of Order-integrals in Lattice Spaces," Mathematics and Statistics, Vol. 11, No. 3, pp. 528 - 533, 2023. DOI: 10.13189/ms.2023.110308.

(b). APA Format:
Mimoza Shkembi , Stela Ceno , John Shkembi (2023). Some Convergence Results for the Strong Versions of Order-integrals in Lattice Spaces. Mathematics and Statistics, 11(3), 528 - 533. DOI: 10.13189/ms.2023.110308.