On Kurzweil-Stieltjes integral in a Banach space

Volterra-stieltjes Integral Equation in Reflexive Banach Spaces

Volterra-Stieltjes integral equations have been studied in the space of continuous functions in many papers for example, (see [3]-[7]). Our aim here is to studing the existence of weak solutions to a nonlinear integral equation of Volterra-Stieltjes type in a reflexive Banach space. A special case will be considered.

Henstock-Kurzweil Integral Transforms

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...

Quadratic Integral Equations in Reflexive Banach Space

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

A Nonexistence Result for the Kurzweil Integral

It is shown that there exist a continuous function f and a regulated function g defined on the interval [0, 1] such that g vanishes everywhere except for a countable set, and the K-integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.