The fuzzy Henstock-Kurzweil delta integral on time scales

Abstract

We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK $\Delta$-integral) on time scales, and obtain two necessary and sufficient conditions for FHK $\Delta$-integrability. The concept of uniformly FHK $\Delta$-integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK $\Delta$-integral.

This is a preprint of a paper whose final and definite form will appear in 'Springer Proceedings in Mathematics and Statistics', ISSN: 2194-1009. Submitted 30-July-2017; accepted 29-Nov-2017

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