It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f : [0, 1] −→ and a continuous function F : [0, 1] −→ such that

We present an existence result for first order dynamic inclusions on time scales with a periodic boundary value condition, assuming the existence of a solution tube for the considered inclusion and the Henstock integrability of the multifunction on the right-hand side.

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

Riemann, Lebesgue, Denjoy, Henstock–Kurzweil, McShane, Feynman, Bochner. There are well over 100 named integrals. Why so many? Some are of historical interest and have been superseded by better, newer ones. The Harnack integral is subsumed by the Denjoy. Some are equivalent, as are McShane and Lebesgue in Rn, and Denjoy, Perron, Henstock–Kurzweil in R. Some are designed to work in special space...

In [8] and [9] J. Jarník and J.Kurzweil introduced an integration process (called PU-integral) for real valued functions on an interval of n with the use of suitably regularC-partitions of unity, instead of the usual partitions. The PU-integral is nonabsolutely convergent and in dimension one falls properly in between the Lebesgue and the Kurzweil-Henstock integrals. In [4], without assuming an...

In this paper, we propose some new concepts for the sequence of fuzzy-number-valued functions by using notion inner small variation. Then, study characteristics primitives strong fuzzy variational Henstock integrals defined in m-dimensional Euclidean space these concepts. Finally, obtain convergence theorems integrals.