Related papers: Global approximation theorems for general gamma ty…
We study the universal approximation properties of transformers and neural integral operators for operators in Banach spaces. In particular, we show that the transformer architecture is a universal approximator of integral operators between…
A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
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 short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order…
We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New…
We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping. Moreover, we introduce and study a method for operator learning in Banach spaces…
Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
In this paper, we introduce a Kantorovich type generalization of Jakimovski-Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) and the theorems on convergence and the degrree of convergence are established. Furthermore,…
In the present paper, we introduce the generalized form of $(p,q)$ Baskakov-Durrmeyer Operators with Stancu type parameters. We derived the local and global approximation properties of these operators and obtained the convergence rate and…