81 Results Found

In this survey, we review the historical development for the Carleson problem about the a.e. pointwise convergence in five aspects: the a.e. convergence for generalized Schrödinger operators along vertical lines; a.e. convergence for Schröd...

The behavior of a new modification of operators of the Baskakov–Schurer–Stancu variant is discussed in this study. First, we establish certain necessary moment and central moment estimates. We then demonstrate the weighted approximation r...

We propose the $\lambda$-Baskakov operator based on $\lambda$-binomial distribution, which is a new Baskakov-type operator. First, the moments and the central moments for them and their quantitative properties are computed. Second, we obtain the rate o...

From Kemp [1], we have a family of confluent q-Chu- Vandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distri...

This work aims to provide several versions of Dini’s theorem for fuzzy number-valued continuous functions defined on a compact set K. In this context, there is a wide variety of possibilities since, unlike the real line, we can consider differe...

This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise err...

Convex relaxations of functions are used to provide bounding information to deterministic global optimization methods for nonconvex systems. To be useful, these relaxations must converge rapidly to the original system as the considered domain shrinks...

In this paper with 1 < p^- ≤ p⁺ <∞ condition we prove a weak convergence result under pointwise convergence and bounded of the sequence. Our theorem is an extension of classical result to variable exponent setting.

In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. I...

In this paper, we expose the ideas of point-wise statistical convergence, equi-statistical convergence and uniform statistical convergence in the sense of the deferred power-series method. We then propose a relation connecting them, which is followed...

Let $\mathcal{A}$ be an algebra of subsets of a set $\mathsf{\Omega }$ and $ba\left(\mathcal{A}\right)$ the Banach space of bounded finitely additive scalar-valued measures on $\mathcal{A}$ endowed with the variation norm. A subset $\mathcal{B}$ of $\mathcal{A}$ is a Nikodým set for $ba\left(\mathcal{A}\right)$ if each countable $\mathcal{B}$-pointwise bound...

This paper introduces a new class of King-type wavelet-assisted Kantorovich q-Baskakov operators, built to address the observation that classical operators of this type typically fail to reproduce the quadratic test function exactly. Moment formulas...

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator ${\widehat{\mu }}_n$ for an unknown mutation rate $\mu$ of microorganisms. Previously, we proved that the associated sequence of estimators $\left\{{\widehat{\mu }}_n\right\}$ con...

For nonparametric regression estimation, conventional research all focus on isotropic regression function. In this paper, a linear wavelet estimator of anisotropic regression function is constructed, the rate of convergence of this estimator is discu...

This research work focuses on $\lambda$-Szász–Mirakjan operators coupling generalized beta function. The kernel functions used in $\lambda$-Szász operators often possess even or odd symmetry. This symmetry influences the behavior of the operator in terms of approxim...

In the present paper, we give an operator with the help of a generalization of Boas–Buck type polynomials by means of Gamma function. We have approximation properties and moments. The rate of convergence is given by the Ditzian–Totik first order modu...

Mean curvature flow (MCF) is an effective tool for investigating the geometry and topology of submanifolds under suitable curvature pinching conditions. While most existing convergence results in complex projective spaces rely on pointwise curvature...

This paper deals not only with pointwise and uniform convergence but also Y-valued fractional approximation results by univariate symmetrized neural network (SNN) operators on Banach space $\left(Y,∥.∥\right)$. Moreover, our main motivation in this work is to compare...

This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the com...

We develop a comprehensive dynamic Walrasian framework entirely in $L^{\infty }$ so that prices and allocations are essentially bounded, and market clearing holds pointwise almost everywhere. Utilities are allowed to be locally Lipschitz and quasi-concave...

In this article, we study the approximation properties of activated singular integral operators over the real line. We establish their convergence to the unit operator with rates. The kernels here derive from neural network activation functions and t...

We call a subset $\mathcal{M}$ of an algebra of sets $\mathcal{A}$ a Grothendieck set for the Banach space $ba\left(\mathcal{A}\right)$ of bounded finitely additive scalar-valued measures on $\mathcal{A}$ equipped with the variation norm if each sequence ${\left\{{\mu }_n\right\}}_{n=1}^{\&}$...

This paper presents a tracking controller for nonlinear systems with matched uncertainties based on contraction metrics and disturbance estimation that provides exponential convergence guarantees. Within the proposed approach, a disturbance estimator...

Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrödinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states (generated...

In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider...

This paper analyzes the exponential convergence properties of Symmetric Stochastic Bernstein Polynomials (SSBPs), a novel approximation framework that combines the deterministic precision of classical Bernstein polynomials (BPs) with the adaptive nod...

Basic fuzzy multicomposite neural network operators are interpreted as fuzzy positive linear operators, and the related general fuzzy theory is applied. These fuzzy operators are defined by the composition of seven well-known activation functions. We...

This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of ${\mathbb{R}}^{\overline{N}}$, $\overline{N}\in \mathbb{N}$. Moreover, we consider the case of approximation employing...

This article proposes a unified concept of topological types of convergence for nets of multifunctions between topological spaces. Any kind of convergence is representable by a (2n + 2)-tuple, n = 0, 1, …, of two special functions u and l, suc...

This paper develops a fully discrete finite element scheme for the fractional wave equation with order $\alpha \in (1,2)$, whose solution typically exhibits a weak singularity near the initial time $t=0$. By introducing an auxiliary variable, we first...

In this work we study the univariate and multivariate quantitative approximation by multi-composite Kantorovich–Choquet-type quasi-interpolation neural network operators with respect to the supremum norm. This is achieved with rates via the fir...

We study whether overparameterized neural networks can learn to satisfy pointwise constraints without inductive bias. One might expect that a sufficiently expressive network would learn to respect such constraints. We prove that this is not the case....

In this article, two classes of sufficient conditions of weak solutions are given to guarantee the energy conservation of the compressible Euler equations. Our strategy is to introduce a test function $\phi \left(t\right)v^{ϵ}$ to derive the total energy. The...

This paper presents a finite difference approach for solving the time-fractional Burgers’ equation, which is a model for nonlinear flow with memory effects. The method leverages the $L1-2$ formula for the fractional derivative and provides a nove...

In this article we present the multivariate approximation of time splitting random functions defined on a box or ${\mathbb{R}}^N,N\in \mathbb{N},$ by neural network operators of quasi-interpolation type. We achieve these approximations by obtaining quantitative-type Jack...

In this work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space with domain on a closed interval or all reals, by quasi-interpolation neural network operators...

Stute presented the so-called conditional U-statistics generalizing the Nadaraya–Watson estimates of the regression function. Stute demonstrated their pointwise consistency and the asymptotic normality. In this paper, we extend the results to a...

In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields...

Time-fractional generalizations of the Lindblad master equation describe open quantum systems whose coupling to the environment exhibits power-law memory. We develop the optimal-control theory of such systems and analyse the consistency of the adjoin...

This paper presents a contraction-based learning control architecture that allows for using model learning tools to learn matched model uncertainties while guaranteeing trajectory tracking performance during the learning transients. The architecture...

The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions. The time Gerasimov-Caputo derivative is discretized by the L1 scheme on a graded mesh...

This paper develops a pointwise distributional theory for linear wavelet density and regression estimation from randomly right-censored observations exhibiting stationary ergodic dependence. In contrast to the prevailing literature, which typically r...

We formulate and analyze a new finite difference scheme for a shallow water model in the form of viscous Burgers-Poisson system with periodic boundary conditions. The proposed scheme belongs to a family of three-level linearized finite difference met...

A subset $\mathcal{B}$ of an algebra $\mathcal{A}$ of subsets of a set $\Omega$ has property $\left(N\right)$ if each $\mathcal{B}$-pointwise bounded sequence of the Banach space $ba\left(\mathcal{A}\right)$ is bounded in $ba\left(\mathcal{A}\right)$, where $ba\left(\mathcal{A}\right)$ is the Banach space of real or complex bounded finitely additive measures defined on $\mathcal{A}$ e...

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-...

Exceptional points are parameter values at which two eigenvalues and their corresponding eigenfunctions coalesce, rendering the wave operator defective. They arise widely in non-Hermitian wave physics and disrupt the modal expansions on which semi-an...

This paper investigates optimal resource allocation in multi-agent networks subject to simultaneous measurement and communication delays. We propose a distributed stochastic extremum seeking (SES) algorithm for connected undirected graphs with hetero...

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asym...

This study introduces an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically. The goal is to partition...

In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise con...