Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...

We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Some versions of the formula of integration by parts with respect to the Henstock-Kurzweil and the Henstock-Stieltjes integrals in Riesz spaces are given.

This paper deals with a new Henstock-Kurzweil integral in Banach Space Bilinear triple n-tuple and integrator function Ψ which depends on multiple points partition. Finally, exhibit standard results of Generalized Henstock - Kurzweil the theory integration.

When a real-valued function of one variable is approximated by its n th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f (n) or f (n+1) are Henstock–Kurzweil integrable. When the only assumption is that f (n) is Henstock–Kurzweil integrable then a modified form of the n th degree Taylor polynomial is used. When the only assumption i...

In this paper, we prove the existence of continuous solutions of a Volterra integral inclusion involving the Henstock-Kurzweil-Pettis integral. Since this kind of integral is more general than the Bochner, Pettis and Henstock integrals, our result extends many of the results previously obtained in the single-valued setting or in the set-valued case.