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In this work, we give well-known results related to some properties, dual spaces and matrix transformations of the sequence space bv and introduce the matrix domain of space bv with arbitrary triangle matrix A. Afterward, we choose the…

This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems…

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…

The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…

New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth order elliptic equation. We also obtain…

We construct the analogue of the Serre spectral sequence for the bounded cohomology of simplicial sets with seminormed local coefficients. As applications, we obtain a (non-isometric) generalization of Gromov's mapping theorem and some…

We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…

Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations…

Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…

In this paper, we present a complete spectral research of generalized Ces\`aro operators on Sobolev-Lebesgue sequence spaces. The main idea is to subordinate such operators to suitable $C_0$-semigroups on these sequence spaces. We introduce…

The Chebyshev polynomials are utilized in this study to define the subclass of the bi-univalent function. Also, Chebyshev polynomial bounds and Fekete-Szego inequalities for functions defined in the classes are established.

We obtain an interesting inequalities for uniformly continuous functions in the normed spaces: $\|f(x)\|\leq a\|x\|+b$ for some $a,b> 0$.

Relying on Kolmogorov's classical characterization of normable Topological Vector spaces, we study the normability of those Probabilistic Normed Spaces that are also Topological Vector spaces and provide a characterization of normable…

In this note a criterion for Cauchy sequences is proved which refines the one presented in `Cauchy sequences in b-metric spaces', Topology Appl. 373 (2025) 109477.

In this paper we present full characterizations of multifunctions admitting a measurable by seminorm selector in Frechet spaces.

Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of $\mathbb R^n$ endowed with measures whose decay on balls is dominated by a power $d$ of their radius. Norms in arbitrary rearrangement-invariant…

We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…