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.

scholarly journals A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Fatma Taşdelen ◽  
Rabia Aktaş ◽  
Abdullah Altın
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Classical Approach ◽  
Type Result ◽  
Convergence Properties ◽  
Szász Operators ◽  
Korovkin’S Theorem ◽  
Second Modulus Of Continuity

We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.

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 Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0

2019 ◽  
Vol 12 (4) ◽  
pp. 1508-1523 ◽  
Author(s):  
Ali Jassim Mohammad ◽  
Hadeel Omar Muslim
Keyword(s):  
Asymptotic Formula ◽  
Modulus Of Continuity ◽  
Convergence Theorem ◽  
Simultaneous Approximation ◽  
Test Functions ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Numerical Examples ◽  
Szász Operators ◽  
Better Than

In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators  on the interval . It turns out that, the sequence  gives better than the results of the sequence  for the two test functions using in the numerical examples.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

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.

scholarly journals Approximation of General Form for a Sequence of Linear Positive Operators Based on Four Parameters

2018 ◽  
Vol 14 (2) ◽  
pp. 7921-7936
Author(s):  
Khalid Dhaman Abbod ◽  
Ali J. Mohammad
Keyword(s):  
Asymptotic Formula ◽  
Weight Function ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Simultaneous Approximation ◽  
Positive Operators ◽  
Order Moment ◽  
Linear Positive Operators ◽  
Numerical Examples

In the present paper, we define a generalization sequence of linear positive operators based on four parameters which is reduce to many other sequences of summation–integral older type operators of any weight function (Bernstein, Baskakov, Szász or Beta). Firstly, we find a recurrence relation of the -th order moment and study the convergence theorem for this generalization sequence. Secondly, we give a Voronovaskaja-type asymptotic formula for simultaneous approximation. Finally, we introduce some numerical examples to view the effect of the four parameters of this sequence.

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.

scholarly journals The Voronovskaja theorem for some linear positive operators defined by infinite sum

2011 ◽  
Vol 20 (1) ◽  
pp. 55-61
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Type Theorem ◽  
Positive Operators ◽  
Linear Positive Operators ◽  
Szász Operators ◽  
Voronovskaja Type Theorem ◽  
Infinite Sum

The main goal of this paper is to establish a Voronovskaja type theorem for the Szasz-Mirakjan-Schurer operators. As a particular case, we get also the Voronovskaja type theorem for the well known Mirakjan-Favard-Szasz operators.

scholarly journals A new modification of Durrmeyer type mixed hybrid operators

2018 ◽  
Vol 34 (1) ◽  
pp. 47-56
Author(s):  
ARUN KAJLA ◽  
◽  
TUNCER ACAR ◽  
Keyword(s):  
General Class ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Linear Positive Operators ◽  
Szász Operators ◽  
Voronovskaja Type Theorem ◽  
Integrable Functions ◽  
Durrmeyer Variant

In 2008 V. Mihes¸an constructed a general class of linear positive operators generalizing the Szasz operators. In ´ this article, a Durrmeyer variant of these operators is introduced which is a method to approximate the Lebesgue integrable functions. First, we derive some indispensable auxiliary results in the second section. We present a quantitative Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

Blending type approximation by generalized Szász type operators based on Charlier polynomials

2018 ◽  
Vol 27 (1) ◽  
pp. 49-56
Author(s):  
ARUN KAJLA ◽  
Keyword(s):  
Rate Of Convergence ◽  
Weighted Approximation ◽  
Type Result ◽  
Weighted Modulus Of Continuity ◽  
Charlier Polynomials ◽  
Weighted Function ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Weighted Function Space ◽  
Weighted Modulus

In the present paper, we introduce a generalized Szasz type operators based on ´ ρ(x) where ρ is a continuously differentiable function on [0, ∞), ρ(0) = 0 and inf ρ 0 (x) ≥ 1, x ∈ [0, ∞). This function not only characterizes the operators but also characterizes the Korovkin set 1, ρ, ρ2 in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.

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