scholarly journals Better approximation of functions by genuine Bernstein-Durrmeyer type operators

2019 ◽  
Vol 35 (2) ◽  
pp. 125-136
Author(s):  
ANA MARIA ACU ◽  
P. N. AGRAWAL ◽  
◽  
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Of Functions ◽  
Numerical Examples ◽  
Durrmeyer Operator ◽  
Durrmeyer Type Operators ◽  
Theoretical Results ◽  
Second Modulus Of Continuity

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.

Bézier variant of Bernstein–Durrmeyer blending-type operators

2021 ◽  
pp. 2250103
Author(s):  
Chandra Prakash ◽  
Naokant Deo ◽  
D. K. Verma
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Graphical Representation ◽  
Type Function ◽  
Rate Of Approximation ◽  
Durrmeyer Type Operators ◽  
Derivatives Of ◽  
Theoretical Results ◽  
Bézier Variant

In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators [Formula: see text] using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.

scholarly journals On (p,q)-Analogue of Gamma Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Wen-Tao Cheng ◽  
Wen-Hui Zhang
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation

In this paper, a kind of new analogue of Gamma type operators based on (p,q)-integers is introduced. The Voronovskaja type asymptotic formula of these operators is investigated. And some other results of these operators are studied by means of modulus of continuity and Peetre K-functional. Finally, some direct theorems concerned with the rate of convergence and the weighted approximation for these operators are also obtained.

scholarly journals Approximation by Stancu-Durrmeyer type operators based on Pólya-Eggenberger distribution

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4249-4261
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Bounded Variation ◽  
Modulus Of Smoothness ◽  
Stancu Operators ◽  
Rate Of Approximation ◽  
Durrmeyer Type Operators

In the present paper we introduce the Durrmeyer type modification of Stancu operators based on P?lya-Eggenberger distribution. For these new operators some indispensable auxiliary results are established in the second section. Our further study focuses on a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, respectively Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

scholarly journals Durrmeyer-Type Generalization of Parametric Bernstein Operators

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1141
Author(s):  
Arun Kajla ◽  
Mohammad Mursaleen ◽  
Tuncer Acar
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Bounded Variation ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Type Space ◽  
Rate Of Approximation ◽  
Derivatives Of ◽  
Theoretical Results

In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation for the Lipschitz type space. The Voronovskaja type asymptotic formula and the rate of convergence of functions with derivatives of bounded variation are established. Finally, the theoretical results are demonstrated by using MAPLE software.

scholarly journals Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 915
Author(s):  
Vijay Gupta ◽  
Ana Maria Acu ◽  
Hari Mohan Srivastava
Keyword(s):  
Linear Approximation ◽  
Approximation Theory ◽  
Classical Result ◽  
Baskakov Operators ◽  
Numerical Examples ◽  
Durrmeyer Operators ◽  
Difference Of Operators ◽  
Durrmeyer Type Operators ◽  
The Difference ◽  
Theoretical Results

In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Szász–Mirakyan operators, the difference between the Baskakov and the Szász–Mirakyan–Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupaş–Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.

Some approximation properties of a kind of (p, q)-Phillips operators

2019 ◽  
Vol 69 (6) ◽  
pp. 1381-1394
Author(s):  
Wentao Cheng ◽  
Chunyan Gui ◽  
Yongmo Hu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Phillips Operators

Abstract In this paper, a kind of new analogue of Phillips operators based on (p, q)-integers is introduced. The moments of the operators are established. Then some local approximation for the above operators is discussed. Also, the rate of convergence and weighted approximation by these operators by means of modulus of continuity are studied. Furthermore, the Voronovskaja type asymptotic formula is investigated.

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 Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhi-Peng Lin ◽  
Wen-Tao Cheng ◽  
Xiao-Wei Xu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Gamma Function ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Durrmeyer Operators

In this article, we introduce a new Durrmeyer-type generalization of p , q -Szász-Mirakjan operators using the p , q -gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K -functional. Finally, the rate of convergence and weighted approximation of these operators are presented.

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

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