In this paper we prove existence theorems for integro – differential equations x(t) = f(t, x(t), ∫ t 0 k(t, s, x(s))∆s), x(0) = x0 t ∈ Ia = [0, a] ∩ T, a ∈ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil d...

Using a Riemann-Lebesgue lemma for the Fourier transform over the class of bounded variation functions that vanish at infinity, we prove the Dirichlet–Jordan theorem for functions on this class. Our proof is in the Henstock–Kurzweil integral context and is different to that of Riesz-Livingston [Amer. Math. Monthly 62 (1955), 434–437]. As consequence, we obtain the Dirichlet–Jordan theorem for f...

We introduce the notion of scalar fuzzy McShane and Henstock integrals for number valued functions we discuss their relationship give a version Gordon theorem [24].

It is shown that the upper and lower Henstock integrals coincide with upper and lower Perron integrals, when the former exist.

In this paper, the Henstock integral for fuzzy-number-valued functions in R is defined and some properties of this integral are discussed. Finally, by using the embedding theorem the fuzzy number space E can be embedded into a concrete space, some characterized theorems for this integral are given. AMS Subject Classification: 94D05, 46S40, 47S40, 54A40

Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is function defined in complete $ \Omega \tau vector \mathbb{R} taking values $X$. f ap-Sequential Henstock integrable with respect to $\tau$, Topological $\tau$? It the purpose of this paper proffer affirmative answer question.