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 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 Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3265-3273
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Charlier Polynomials ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In the present paper we introduce the B?zier variant of the Sz?sz-Durrmeyer type operators, involving the Poisson-Charlier polynomials. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness and the rate of convergence for differential functions whose derivatives are of bounded variation.

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 A Kantorovich type integral modification of q-Bernstein-Schurer operators

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1335-1348
Author(s):  
Asha Gairolaa ◽  
Vishnu Mishra ◽  
Karunesh Singh
Keyword(s):  
Asymptotic Formula ◽  
Error Estimates ◽  
Modulus Of Smoothness ◽  
Rate Of Approximation ◽  
Integrable Functions ◽  
Type Integral

The q-Bernstein-Schurer summation type operators are modified in order to make them applicable for approximation of integrable functions. The aim of the paper is twofold. Firstly, to find refined error estimates, |S*(?,?) n,p,q(f)(x) - f(x)| without using Schwarz?s inequality. Secondly, to obtain a generalized Voronovskaya type asymptotic formula. The rate of approximation in terms of modulus of smoothness are also established.

scholarly journals Bivariate-Schurer-Stancu operators based on (p,q)-integers

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1251-1258 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Uniform Approximation ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Korovkin Type Theorem ◽  
Stancu Operators

The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.

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 Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lahsen Aharouch ◽  
Khursheed J. Ansari ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Modulus Of Smoothness ◽  
Weighted Modulus Of Continuity ◽  
Type Formula ◽  
Weighted Modulus ◽  
Bézier Variant

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

scholarly journals Direct estimates for Lupaş-Durrmeyer operators

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 191-199 ◽  
Author(s):  
Ali Aral ◽  
Vijay Gupta
Keyword(s):  
Asymptotic Formula ◽  
Hypergeometric Function ◽  
Bounded Variation ◽  
Open Problem ◽  
Bernstein Polynomials ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Polya Distribution ◽  
Convergence Estimates

The generalization of the Bernstein polynomials based on Polya distribution was first considered by Stancu [14]. Very recently Gupta and Rassias [6] proposed the Durrmeyer type modification of the Lupa? operators and established some results. Now we extend the studies and here we estimate the convergence estimates, which include quantitative asymptotic formula and rate of approximation bounded variation. We also give an open problem for readers to obtain the moments using hypergeometric function.

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