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Sokol Bush Kaliaj

Publications and source records attributed to Sokol Bush Kaliaj.

9 recordsLinked to original sources
arXiv2022

A New Class of Locally Convex Spaces with application

In this paper we define the Radon-Nikodym class (RN class) of locally convex topological vector spaces. The RN class is characterized in terms of the Radon-Nikodym theorem for vector measures using integrable by seminorm derivatives. It is shown that the RNP class of all complete Hausdorff locally convex spaces possessing the Radon-Nikodym property is properly contained in the RN class. As an application we present a Radon-Nikodym theorem for multimeasures with respect to the Pettis integrable multifunctions in terms of the RN class.

math.FA↗
arXiv2020

An integral Suzuki-type fixed point theorem with application

In this paper, we present an integral Suzuki-type fixed point theorem for multivalued mappings defined on a complete metric space in terms of the Ćirić integral contractions. As an application, we will prove an existence and uniqueness theorem for a functional equation arising in dynamic programming of continuous multistage decision processes.

math.FA↗
arXiv2018

Dunford-Henstock-Kurzweil and Dunford-Mcshane integrals of vector-valued functions defined on m-dimensional bounded sets

In this paper, we define the Dunford-Henstock-Kurzweil and the Dunford-McShane integrals of Banach space valued functions defined on a bounded Lebesgue measurable subset of m-dimensional Euclidean space Rm. We will show that the new integrals are "natural" extensions of the McShane and the Henstock-Kurzweil integrals from m-dimensional closed non-degenerate intervals to m-dimensional bounded Lebesgue measurable sets. As applications, we will present full descriptive characterizations of the McShane and Henstock-Kurzweil integrals in terms of our integrals. Moreover, a relationship between new integrals will be proved in terms of the Dunford integral.

math.FA↗
arXiv2016

Full characterizations of the variational McShane Integral on $m$-dimensional compact intervals

In this paper we consider the additive interval functions defined on the family $\mathcal{I}_{m}$ of all non-degenerate closed subintervals of the cubic interval $C_{m} = [0,1]^{m}$ in the $m$-dimensional Euclidean space $\mathbb{R}^{m}$ and taking values in a Banach space $X$. We give necessary and sufficient conditions for an additive interval function $F : \mathcal{I}_{m} \to X$ to be the primitive of a variational McShane (or strong McShane) integrable function $f : C_{m} \to X$ in terms of the convex cubic average range of $F$.

math.FA↗