相关论文: Curves defined by a class of discrete operators: a…
There are many results on the simultaneous approximation by sequences of special positive linear operators. In the year 1978, Ismail and May as well as Volkov independently studied operators of exponential type covering the most classical…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling…
On the one hand, the framework of mixed norm spaces has potential applications in different areas of mathematics. On the other hand, neural network (NN) operators are well established as approximators, attracting significant attention in…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
We introduce certain modified Sz\'{a}sz-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators.
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
Here we research the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation, Baskakov type and quadrature type neural network operators. We…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized…
In this paper, we introduce a Kantorovich type generalization of q-Bernstein-Stancu operators. We study the convergence of the introduced operators and also obtain the rate of convergence by these operators in terms of the modulus of…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
In the present note, we give the generalization of $\alpha-$Baskakov Durrmeyer operators depending on a real parameter $\rho$ > 0. We present the approximation results in Korovkin and weighted Korovkin spaces. We also prove the order of…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
We consider the eigenvalue equation for the largest eigenvalue of certain kinds of non-compact linear operators given as the sum of a multiplication and a kernel operator. It is shown that, under moderate conditions, such operators can be…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…