Global Approximation Theorems for the Szász-Mirakjan Operators in Exponential Weight Spaces

1978 ◽  
pp. 319-333 ◽  
Author(s):  
M. Becker ◽  
D. Kucharski ◽  
R. J. Nessel
Keyword(s):  
Exponential Weight ◽  
Global Approximation ◽  
Approximation Theorems

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 316 ◽  
Author(s):  
Hari Srivastava ◽  
Faruk Özger ◽  
S. Mohiuddine
Keyword(s):  
Uniform Convergence ◽  
Shape Parameter ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Approximation Result ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Direct Approximation

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

scholarly journals Quantitative estimates for the Lupaş q-analogue of the Bernstein operator

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Quantitative Estimates ◽  
Quantitative Results

AbstractWe establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupaş in 1987 and for the approximation properties of the limit Lupaş operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems.

scholarly journals Approximation Theorems for the Schrödinger Equation and Quantum Vortex Reconnection

2021 ◽  
Author(s):  
Alberto Enciso ◽  
Daniel Peralta-Salas
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Chemical Potential ◽  
Quantitative Result ◽  
Pitaevskii Equation ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Quantum Vortex ◽  
Whole Process ◽  
Wide Range

AbstractWe prove the existence of smooth solutions to the Gross–Pitaevskii equation on $$\mathbb {R}^3$$ R 3 that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits to describe the reconnection events in detail and verify that this scenario exhibits the properties observed in experiments and numerics, such as the $$t^{1/2}$$ t 1 / 2 and change of parity laws. We are mostly interested in solutions tending to 1 at infinity, which have finite Ginzburg–Landau energy and physically correspond to the presence of a background chemical potential, but we also consider the cases of Schwartz initial data and of the Gross–Pitaevskii equation on the torus. In the proof, the Gross–Pitaevskii equation operates in a nearly linear regime, so the result applies to a wide range of nonlinear Schrödinger equations. Indeed, an essential ingredient in the proofs is the development of novel global approximation theorems for the Schrödinger equation on $$\mathbb {R}^n$$ R n . Specifically, we prove a qualitative approximation result that applies for solutions defined on very general spacetime sets and also a quantitative result for solutions on product sets in spacetime $$D\times \mathbb {R}$$ D × R . This hinges on frequency-dependent estimates for the Helmholtz–Yukawa equation that are of independent interest.

On generalized Szász-Mirakyan operators of functions of two variables

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Lucyna Rempulska ◽  
Szymon Graczyk
Keyword(s):  
Exponential Weight ◽  
Approximation Theorems ◽  
Functions Of Two Variables

AbstractWe introduce certain generalized Szász-Mirakyan operators in exponential weight spaces of functions of two variables and we give approximation theorems for them.

scholarly journals Approximation theorems for q-Bernstein-Kantorovich operators

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 721-730 ◽  
Author(s):  
Nazim Mahmudov ◽  
Pembe Sabancigil
Keyword(s):  
Type Theorem ◽  
Approximation Properties ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present paper we introduce a q-analogue of the Bernstein-Kantorovich operators and investigate their approximation properties. We study local and global approximation properties and Voronovskaja type theorem for the q-Bernstein-Kantorovich operators in case 0 < q < 1.

Sign in / Sign up

Export Citation Format

Share Document