An asymptotic formula for a class of approximation processes of King’s type

2010 ◽  
Vol 47 (4) ◽  
pp. 435-444 ◽  
Author(s):  
Octavian Agratini
Keyword(s):  
Asymptotic Formula ◽  
General Class ◽  
Weighted Space ◽  
Type Result ◽  
Korovkin Theorem ◽  
Linear Positive Operators ◽  
Approximation Process ◽  
Test Function ◽  
The Third ◽  
Discrete Type

In this paper we present a general class of linear positive operators of discrete type reproducing the third test function of Korovkin theorem. In a certain weighted space it forms an approximation process. A Voronovskaja-type result is established and particular cases are analyzed.

scholarly journals Linear operators that preserve some test functions

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Linear Operators ◽  
Test Functions ◽  
Korovkin Theorem ◽  
Linear Positive Operators ◽  
Test Function ◽  
The Third ◽  
Quantitative Estimates ◽  
Degree Of Exactness ◽  
Abstract Spaces

The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abstract spaces. Particular classes are also studied.

scholarly journals On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sezgin Sucu ◽  
Gürhan İçöz ◽  
Serhan Varma
Keyword(s):  
Convergence Theorem ◽  
Quantitative Estimation ◽  
Laguerre Polynomials ◽  
Classical Approach ◽  
Type Result ◽  
Linear Positive Operators ◽  
Approximation Process ◽  
Charlier Polynomials ◽  
Szász Operators ◽  
Second Modulus Of Continuity

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

King type generalization of Baskakov operators based on (𝑝, 𝑞) calculus with better approximation properties

Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 163-173
Author(s):  
Lakshmi Narayan Mishra ◽  
Shikha Pandey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Modulus Of Continuity ◽  
Research Area ◽  
Positive Operators ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Result ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Test Function

AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

scholarly journals Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

2021 ◽  
pp. 1666-1674
Author(s):  
Ali J. Mohammad ◽  
Amal K. Hassan
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Linear Operators ◽  
Order Of Approximation ◽  
Integral Type ◽  
Test Function ◽  
Numerical Example ◽  
First Derivative ◽  
Two Parameters

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters. 

THE THIRD LAW OF THERMODYNAMICS

1987 ◽  
Vol 01 (01n02) ◽  
pp. 61-66 ◽  
Author(s):  
JACEK MIĘKISZ ◽  
CHARLES RADIN
Keyword(s):  
General Class ◽  
Finite Range ◽  
Zero Temperature ◽  
One Dimensional ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
Third Law

We consider a very general class of discrete classical one dimensional statistical mechanical models and prove that generic finite range interactions have crystalline zero temperature ensembles, and in particular satisfy the third law of thermodynamics.

scholarly journals Asymptotic Formulae via a Korovkin-Type Result

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Daniel Cárdenas-Morales ◽  
Pedro Garrancho ◽  
Ioan Raşa
Keyword(s):  
Positive Operators ◽  
Type Result ◽  
Linear Positive Operators ◽  
Asymptotic Formulae

We present a sort of Korovkin-type result that provides a tool to obtain asymptotic formulae for sequences of linear positive operators.

Approximation by Stancu–Chlodowsky type λ-Bernstein operators

2020 ◽  
Vol 26 (1) ◽  
pp. 97-110
Author(s):  
M. Mursaleen ◽  
A. A. H. Al-Abied ◽  
M. A. Salman
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Direct Result ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin’S Theorem

AbstractIn this paper, we give some approximation properties by Stancu–Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.

scholarly journals The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Behar Baxhaku ◽  
Artan Berisha
Keyword(s):  
Statistical Convergence ◽  
Weighted Space ◽  
Type Result ◽  
Positive Semiaxis

We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given.

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