Related papers: Remarks on the Ostrovsky's Theorem

We study the problem of the existence of increasing and continuous solutions $\varphi\colon[0,1]\to[0,1]$ such that $\varphi(0)=0$ and $\varphi(1)=1$ of the functional equation \begin{equation*}…

In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of…

Existence of symmetric (resp. asymmetric) solutions to the $L_p$ Gaussian Minkowski problem for $p\leq 0$ (resp. $p\geq 1$) will be provided. Moreover, existence and uniqueness of smooth solutions to the problem for $p>n$ will also be…

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions…

We prove that every 0/1-polytope has a unique Minkowski decomposition into indecomposable polytopes, up to translation of summands. The summands lie in pairwise orthogonal subspaces. Thus, every 0/1-polytope is the Cartesian product of…

We shall firstly study the existence of one positive solution of a model problem for one equation via the classical Krasnosel'ski\u\i{} fixed-point theorem. Secondly we investigate how to handle this problem via the fixed point index theory…

We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary,…

The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is…

We show that a topometric space $X$ is topometrically isomorphic to a type space of some continuous first-order theory if and only if $X$ is compact and has an open metric (i.e., satisfies that $\{p : d(p,U) < \varepsilon\}$ is open for…

A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topological group G is g-reversible if every continuous automorphism…

The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive,…

This paper is devoted to the investigation of an important issue recently brought into attention by a recent paper of Arutyunov: the relation between openness of composition of set-valued maps and fixed point results. More precisely, we…

In this paper, we establish Luzin's condition (N) for mappings in certain Sobolev-Orlicz spaces with certain moduli of continuity. Further, given a mapping in these Sobolev-Orlicz spaces, we give bounds on the size of the exceptional set…

In this paper we investigate a conjecture of Janusz Matkowski concerning the continuous solutions of the functional equation \[ f\big(f(-x)+x\big)=f\big(-f(x)\big)+f(x),\qquad x\in\mathbb{R}. \] Matkowski conjectured that all continuous…

The question of triviality of solutions of the semilinear Ornstein-Uhlenbeck equation, \[ \Delta w-\frac{1}{2} \langle x,\nabla w\rangle-\frac{\lambda}{p-1}w+|w|^{p-1}w=0, \] is considered. It is shown, that if $p>1$ is Sobolev subcritical…

Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2.

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

We study the local behavior of the closed-open discrete maps of Orlich--Sobolev classes in ${\Bbb R}^n,$ $n\geqslant 3.$ It was found that these mappings $f$ have continuous extension in isolated point $x_0$ in $D\setminus\{x_0 \},$ as soon…

We prove that if $M$ and $N$ are Riemannian, oriented $n$-dimensional manifolds without boundary and additionally $N$ is compact, then Sobolev mappings $W^{1,n}(M,N)$ of finite distortion are continuous. In particular, $W^{1,n}(M,N)$…

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…