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.

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 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 On Rate of Approximation by Modified Beta Operators

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Prerna Maheshwari (Sharma) ◽  
Vijay Gupta
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Rate Of Approximation ◽  
Derivatives Of

We establish the rate of convergence for the modified Beta operators , for functions having derivatives of bounded variation.

scholarly journals Rate of Convergence for Ibragimov-Gadjiev-Durrmeyer Operators

2017 ◽  
Vol 50 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Durrmeyer Operators ◽  
Special Cases ◽  
Derivatives Of

Abstract The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

scholarly journals Simultaneous Approximation for Generalized Srivastava-Gupta Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Tuncer Acar ◽  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Simultaneous Approximation ◽  
Integrable Functions ◽  
Derivatives Of

We introduce a new Stancu type generalization of Srivastava-Gupta operators to approximate integrable functions on the interval0,∞and estimate the rate of convergence for functions having derivatives of bounded variation. Also we present simultenaous approximation by new operators in the end of the paper.

scholarly journals Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 335-343 ◽  
Author(s):  
Arun Kajla ◽  
Serkan Araci
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Smoothness ◽  
Stancu Operators ◽  
Rate Of Approximation ◽  
Type Approximation ◽  
Kantorovich Operators

AbstractIn the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

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.

scholarly journals RateofConvergenceofHermite-Fej´erPolynomialsfor Functions with Derivatives of Bounded Variation

2020 ◽  
Vol 51 (1) ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Chebyshev Polynomials ◽  
Derivatives Of

In this paper, the behavior of the Hermite-Fej´er interpolation for functionswithderivativesofboundedvariationon[−1,1]isstudiedbytakingtheinterpolation over the zeros of Chebyshev polynomials of the second kind. An estimate for the rate of convergence using the zeros of the Chebyshev polynomials of the second kind is given.  

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