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.

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.