We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, [Formula: see text] as [Formula: see text], using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the ...

We give a sufficient and necessary condition such that for almost all s ∈ R ‖nθ − s‖ < ψ(n) for infinitely many n ∈ N, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This improves upon an old result of Kurzweil and contains several previous results as special cases: two theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. Moreover, we also discus...

Existence of the smallest, greatest, minimal, maximal and unique continuous solutions to distributional Cauchy problems, as well as their dependence on the data, are studied. The main tools are a continuous primitive integral and fixed point results in function spaces.

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.

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.

Few today would dispute that the age of autonomous machines is nearly upon us (cf., Kurzweil, 2005; Moravec, 1988), if it not already. While doubtful one can identify any fully autono...

In this paper, we derive regularity estimates for the electric field integral operator which arises when formulating the time-harmonic Maxwell problem as a boundary integral equation. More precisely, we show that the regularity constants can be bounded polynomially in terms of the frequency, where the degree of the polynomial depends on the regularity order and is given explicitly. The paper co...