The Fourier transform is considered as a Henstock–Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann–Lebesgue lemma fails: Henstock– Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appen...

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.

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.

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

Integral Henstock-Kurzweil dapat dikatakan sebagai perumuman dari integral Riemann. ini dikonstruksi berdasarkan partisi yang didefinisikan dengan memodifikasi konstanta pada Riemann menjadi fungsi positif . Pada artikel ini, ditunjukkan sifat-sifat dipenuhi oleh fungsi-fungsi terintegralkan khususnya di ruang berdimensi-n menggunakan norm maksimum. Kemudian pula bahwa setaip kontinu himpunan t...

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

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.

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...