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Marko Kostić

Publications and source records attributed to Marko Kostić.

At least 19 recordsLinked to original sources
arXiv2024

Abstract non-scalar Volterra difference equations

In this paper, we investigate the abstract non-scalar Volterra difference equations. We employ the Poisson like transforms to connect the solutions of the abstract non-scalar Volterra integro-differential equations and the abstract non-scalar Volterra difference equations. We also investigate the existence, uniqueness and almost periodicity of solutions to the abstract multi-term fractional difference equations with Weyl fractional derivatives.

math.GM↗
arXiv2022

Multi-dimensional Besicovitch almost periodic type functions and applications

In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of Besicovitch-Doss almost periodicity in the multi-dimensional setting, and provide some applications of our results to the abstract Volterra integro-differential equations and the partial differential equations.

math.FA↗
arXiv2021

Generalized $c$-almost periodic type functions in ${\mathbb R}^n$

In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$-almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$-almost periodic functions and reconsider the notion of semi-$c$-periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain applications of our results to the abstract Volterra integro-differential equations in Banach spaces.

math.FA↗
arXiv2020

Multi-dimensional $c$-almost periodic type functions and applications

In this paper, we analyze multi-dimensional Bohr $({\mathcal B},c)$-almost periodic type functions. The main structural characterizations for the introduced classes of Bohr $({\mathcal B},c)$-almost periodic type functions are established. Several applications of our abstract theoretical results to the abstract Volterra integro-differential equations in Banach spaces are provided, as well.

math.FA↗
arXiv2020

Semi-Bloch periodic functions, semi-anti-periodic functions and applications

In this paper, we introduce the notions of semi-Bloch periodic functions and semi-anti-periodic functions. Stepanov semi-Bloch periodic functions and Stepanov semi-anti-periodic functions are considered, as well. We analyze the invariance of introduced classes under the actions of convolution products and briefly explain how one can use the obtained results in the qualitative analysis of solutions of abstract inhomogeneous integro-differential equations.

math.FA↗
arXiv2020

Asymptotically Weyl almost periodic functions in Lebesgue spaces with variable exponents

In this paper, we introduce and analyze several different notions of Weyl almost periodic functions and Weyl ergodic components in Lebesgue spaces with variable exponent $L^{p(x)}.$ We investigate the invariance of (asymptotical) Weyl almost periodicity with variable exponent under the actions of convolution products, providing also some illustrative applications to abstract fractional differential inclusions in Banach spaces. The introduced classes of generalized (asymptotically) Weyl almost periodic functions are new even in the case that the function $p(x)$ has a constant value $p\geq 1,$ provided that the functions $ϕ(x)$ and $F(l,t)$ under our consideration satisfy $ϕ(x)\neq x$ or $F(l,t)\neq l^{(-1)/p}.$

math.FA↗
arXiv2019

Abstract degenerate Volterra integro-differential equations: inverse generator problem

In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces. The classes of degenerate $(a,k)$-regularized $C$-resolvent families and degenerate mild $(a,k)$-regularized $(C_{1},C_{2})$-existence and uniqueness families play an important role in our analysis. We provide several illustrative applications of obtained theoretical results, primarily to abstract degenerate fractional differential equations with Caputo derivatives.

math.FA↗
arXiv2019

New inequalities for the function $y=t\ln t$

The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2020}, is to propose several new inequalities for the function $y=t\ln t.$ We consider the local behaviour of this function near the point $t=1,$ as well as the global behaviour of this function on the intervals $[1,\infty)$ and $(0,1].$

math.GM↗
arXiv2019

Recurrent strongly continuous operator families on Banach space

In this paper, we analyze recurrent $C_{0}$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_{0}$-rigid semigroups of bounded operators and give a structural characterization of them. A characterization of a Li-Yorke chaoticity of the translation semigroup $(T(t))_{t\geq 0}$ on weighted spaces of integrable functions and continuous functions in terms of admissible weight function is given. The recurrent $C_0$-semigroups induced by semiflows are characterized on the spaces of integrable functions and of spaces of continuous functions.

math.FA↗
arXiv2019

Disjoint Li-Yorke chaos in Fréchet spaces

The main aim of this paper is to consider various notions of (dense) disjoint Li-Yorke chaos for general sequences of multivalued linear operators in Fr\' echet spaces. We also consider continuous analogues of introduced notions and provide certain applications to the abstract partial differential equations.

math.FA↗
arXiv2019

Disjoint distributional chaos in Fréchet spaces

We introduce several different notions of disjoint distributional chaos for sequences of multivalued linear operators in Fréchet spaces. Any of these notions seems to be new and not considered elsewhere even for linear continuous operators in Banach spaces. We focus special attention to the analysis of some specific classes of linear continuous operators having a certain disjoint distributionally chaotic behaviour, providing also a great number of illustrative examples and applications of our abstract theoretical results.

math.FA↗
arXiv2019

Reiterative $m_{n}$-distributional chaos of type $s$ in Fr\' echet spaces

The main aim of this paper is to consider various notions of (dense) $m_{n}$-distributional chaos of type $s$ and (dense) reiterative $m_{n}$-distributional chaos of type $s$ for general sequences of linear not necessarily continuous operators in Fr\' echet spaces. Here, $(m_{n})$ is an increasing sequence in $[1,\infty)$ satisfying $\liminf_{n\rightarrow \infty}\frac{m_{n}}{n}>0$ and $s$ could be $0,1,2,2+,2\frac{1}{2},3,1+,2-,2_{Bd},2_{Bd}+.$ We investigate $m_{n}$-distributionally chaotic properties and reiteratively $m_{n}$-distributionally chaotic properties of some special classes of operators like weighted forward shift operators and weighted backward shift operators in Fr\' echet sequence spaces, considering also continuous analogues of introduced notions and some applications to abstract partial differential equations.

math.FA↗
arXiv2019

Reiterative distributional chaos on Banach spaces

If we change the upper and lower density in the definition of distributional chaos of a continuous linear operator on Banach space by the Banach upper and Banach lower density, respectively, we obtain Li-Yorke chaos. Motivated by this fact, we introduce the notions of reiterative distributional chaos of types $1$, $1^+$ and $2$ for continuous linear operators on Banach spaces, which are characterized in terms of the existence of an irregular vector with additional properties. Moreover, we study its relations with other dynamical properties and give conditions for the existence of a vector subspace $Y$ of $X$ such that every non-zero vector in $Y$ is both irregular for $T$ and distributionally near to zero for $T.$

math.FA↗
arXiv2019

Generalized almost periodic and generalized asymptotically almost periodic type functions in Lebesgue spaces with variable exponents $L^{p(x)}$

In the paper under review, we introduce the notions of various types of generalized (asymptotical) almost periodicity with variable exponents. We define and thoroughly analyze an important subclass of (asymptotically) Stepanov almost periodic functions which contains all (asymptotically) almost periodic functions. We provide a great number of relevant applications to abstract Volterra integro-differential equations in Banach spaces.

math.FA↗
arXiv2019

Distributional chaos and Li-Yorke chaos in metric spaces

In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we focus our attention to some special features of distributionally chaotic and Li-Yorke chaotic multivalued linear operators in Frechet spaces.

math.FA↗