Closure properties for integral problems driven by regulated functions via convergence results

Measure Differential Inclusions: Existence Results and Minimum Problems

“…In the case of a finite dimensional space, existence results for this kind of solution can be found for single-valued framework in [19,26] or [21], while for the set-valued setting, when the multifunction G has compact convex values, existence results were proved in [9] under Carathéodory-type assumptions or in [17]. Moreover, well-posedness has been obtained (e.g.…”

“…the Hausdorff-Pompeiu distance, which was traditionally used while studying measure differential inclusions (e.g. in [17,18,34] or [38]).…”

On Regulated Solutions of Impulsive Differential Equations with Variable Times

“…In this paper we study impulsive IVPs in the space G([a, b]) of regulated functions, which seems to be the natural space of solutions for impulsive problems (see [18][19][20]), and we investigate properties of solutions as elements of this space. This allows us to cover and extend earlier approaches.…”

A survey on composition operators on some function spaces

“…are closely related to existence and uniqueness results for solutions of operator equations involving C f and S h . Also, for example, in [29], it is proved, for the integral equation of Volterra type in the Henstock setting, that the existence of a continuous solution depends, among other conditions, on the property of mapping continuous functions into Henstock-integrable functions, satisfied by the involved non-autonomous superposition operator; in [15], the authors provide, in the Henstock-Kurzweil-Pettis setting, existence and closure results for integral problems driven by regulated functions, both in single-and set-valued cases ( [14]). Hence, in many fields of non-linear analysis and its applications (in particular to integral equations), the following problem becomes of interest:…”