Related papers: Some Approximation Properties of the Generalized B…
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results…
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…
In this paper, First we have given the modified form of (p,q)-analogues of Bernstein and Bernstein operators [21-23] and then we introduce a new analogue of Bernstein-Kantorovich operators which we call as (p,q)-Bernstein-Kantorovich…
This research includes the study of some positive sampling Kantorovich operators (SK operators) and their convergence properties. A comprehensive analysis of both local and global approximation properties is presented using sampling…
We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
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 aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer the problem of uniform approximation of continuous functions on closed bounded interval and the problem of…
In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of…
We prove the existence of entire functions that achieve universal approximations on certain countable sequences of translation operators .
In this paper, the method of approximate transformation groups which was proposed by Baikov, Gazizov and Ibragimov, is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended…
In this paper, we introduce new modifications of Szasz-Mirakyan operators based on (p,q)-integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to…
Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich…
In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 437-478 -- see also arXiv:1804.11290), the same authors have studied viscous…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
We generalize the Oka extension theorem, and obtain bounds on the norm of the extension, by using operator theory.
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
The present study offers a general exponential operator connected with a^2+x^2; for positive real "a". We estimate the asymptotic formula for simultaneous and ordinary approximation of the constructed operator. In the last section, we…