scholarly journals Direct local and global approximation theorem for Bernstein-type operators

Filomat ◽  
2004 ◽  
pp. 27-32 ◽  
Author(s):  
Zoltan Finta
Keyword(s):  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Global Approximation ◽  
Bernstein Type ◽  
Global Estimates

Direct local and global estimates are established for Bernstein - type operators using Ditzian - Totik modulus of smoothness of second order.

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 Blending type Approximations by Kantorovich variant of α-Schurer operators

2021 ◽  
Author(s):  
Nadeem Rao ◽  
Pradeep Malik ◽  
Mamta Rani
Keyword(s):  
Numerical Analysis ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Weight Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Global Approximation ◽  
Measurable Functions ◽  
Two Parameters ◽  
Kantorovich Operators

In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetre’s K-functional and weight functions for these sequences in dierent spaces of functions.

scholarly journals A genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2611-2623 ◽  
Author(s):  
Trapti Neer ◽  
P.N. Agrawal
Keyword(s):  
Approximation Theorem ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Global Approximation ◽  
Approximation Of Functions ◽  
Moment Estimates ◽  
Durrmeyer Type Operators ◽  
Direct Results ◽  
Classical Modulus

In this paper, we construct a genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions. We establish some moment estimates and the direct results which include global approximation theorem in terms of classical modulus of continuity, local approximation theorem in terms of the second order Ditizian-Totik modulus of smoothness, Voronovskaya-type asymptotic theorem and a quantitative estimate of the same type. Lastly, we study the approximation of functions having a derivative of bounded variation.

scholarly journals Bezier variant of genuine-Durrmeyer type operators based on Polya distribution

2017 ◽  
Vol 33 (1) ◽  
pp. 73-86
Author(s):  
TRAPTI NEER ◽  
◽  
ANA MARIA ACU ◽  
P. N. AGRAWAL ◽  
◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Global Approximation ◽  
Voronovskaja Type Theorem ◽  
Polya Distribution ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In this paper we introduce the Bezier variant of genuine-Durrmeyer type operators having Polya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for functions whose derivatives are of bounded variation is obtained. Further, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

A Global Approximation Theorem for Meyer-K�nig and Zeller operators

1978 ◽  
Vol 160 (3) ◽  
pp. 195-206 ◽  
Author(s):  
Michael Becker ◽  
Rolf J. Nessel
Keyword(s):  
Approximation Theorem ◽  
Global Approximation

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.

Global smoothness preservation with second order modulus of smoothness

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Gancho Tachev
Keyword(s):  
Modulus Of Smoothness ◽  
Second Order ◽  
Positive Operators ◽  
Bernstein Operator ◽  
Linear Positive Operators ◽  
Global Smoothness Preservation ◽  
Global Smoothness

AbstractWe establish the global smoothness preservation of a function f by the sequence of linear positive operators. Our estimate is in terms of the second order Ditzian-Totik modulus of smoothness. Application is given to the Bernstein operator.

scholarly journals On Approximation by Gupta type general family of Operators

2021 ◽  
Author(s):  
Karunesh Singh
Keyword(s):  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Asymptotic Result ◽  
Linear Positive Operators ◽  
Type Approximation ◽  
Quantitative Form ◽  
Wide Range ◽  
Direct Results

In this paper, we study Gupta type family of positive linear operators, which have a wide range of many well known linear positive operators e.g. Phillips, Baskakov-Durrmeyer, Baskakov-Sz\’{a}sz, Sz\’{a}sz-Beta, Lupa\c{s}-Beta, Lupa\c{s}-Sz\’{a}sz, genuine Bernstein-Durrmeyer, Link, P\u{a}lt\u{a}nea, Mihe\c{s}an-Durrmeyer, link Bernstein-Durrmeyer etc. We first establish direct results in terms of usual modulus of continuity having order 2 and Ditzian-Totik modulus of smoothness and then study quantitative Voronovkaya theorem for the weighted spaces of functions. Further, we establish Gr\“{u}ss-Voronovskaja type approximation theorem and also derive Gr\”{u}ss-Voronovskaja type asymptotic result in quantitative form.

scholarly journals Quantitative results for positive linear operators which preserve certain functions

2019 ◽  
Vol 27 (2) ◽  
pp. 85-95
Author(s):  
Marius-Mihai Birou
Keyword(s):  
Modulus Of Continuity ◽  
Second Order ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Moduli Of Smoothness ◽  
Generalized Modulus Of Continuity ◽  
Bernstein Type ◽  
Quantitative Results ◽  
Durrmeyer Type Operators

AbstractIn this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.

scholarly journals On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Edmond Aliaga ◽  
Behar Baxhaku
Keyword(s):  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Matlab Software ◽  
Type Space ◽  
Mixed Modulus Of Smoothness ◽  
Mixed Modulus ◽  
Boolean Sum

In this article, we establish an extension of the bivariate generalization of the q -Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q -Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate q -Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software.

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