Bibliographic Details
| Title: |
Time Scale Henstock-Kurzweil Integration for Set-Valued Functions. |
| Authors: |
Sekhose, Vikuozonuo1 vikuosekhose4@gmail.com, Bharali, Hemen2 hemen.bharali@gmail.com |
| Source: |
IAENG International Journal of Applied Mathematics. Apr2026, Vol. 56 Issue 4, p1332-1343. 12p. |
| Subjects: |
Integrals, Set functions, Mathematical functions, Convex domains, Hausdorff measures |
| Abstract: |
This paper introduces the Henstock-Kurzweil integration for functions whose values are sets on time scales- the set-valued Henstock-Kurzweil Δ-integral and set-valued Henstock-Kurzweil ∇-integral. Properties of the integral are established. Some key theorems in the paper discusses convexity, relation between set-valued Henstock-Kurzweil integral and ordinary Henstock-Kurzweil integral via support function, singleton set function and Hausdorff metric respectively. The convergence of sequences and series of set-valued Henstock-Kurzweil integrable functions are also formulated. In addition, as a linear combination of the Δ- and ∇-integrals we introduce the set-valued Henstock-Kurzweil ♢α-integral and conclude with a theorem depicting the relation between the three integrals. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
