On Approximation Properties of a New Type of Bernstein-Durrmeyer Operators

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Tuncer Acar ◽  
Ali Aral ◽  
Vijay Gupta
Keyword(s):  
Asymptotic Formula ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Hypergeometric Series ◽  
Approximation Properties ◽  
Global Approximation ◽  
Durrmeyer Operators ◽  
New Type

AbstractThe present paper deals with a new type of Bernstein-Durrmeyer operators on mobile interval. First, we represent the operators in terms of hypergeometric series. We also establish local and global approximation results for these operators in terms of modulus of continuity. We obtain an asymptotic formula for these operators and in the last section we present better error estimation for the operators using King type approach

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 Approximation properties of the new type generalized Bernstein-Kantorovich operators

2021 ◽  
Vol 7 (3) ◽  
pp. 3826-3844
Author(s):  
Mustafa Kara ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Type Theorem ◽  
Numerical Results ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
New Type ◽  
Kantorovich Operators

<abstract><p>In this paper, we introduce new type of generalized Kantorovich variant of $ \alpha $-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $ \alpha $-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.</p></abstract>

scholarly journals On Simultaneous Approximation of Modified Baskakov-Durrmeyer Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Prashantkumar G. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Error Estimation ◽  
Pointwise Convergence ◽  
Simultaneous Approximation ◽  
Second Order ◽  
Durrmeyer Operators

We discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter γ>0. We compute the moments of these modified operators. Also, we establish pointwise convergence, Voronovskaja type asymptotic formula, and an error estimation in terms of second order modification of continuity of the function for the operators Bn,γα,β(f,x).

scholarly journals Quantitative estimates for Szász operators and its hybrid variant

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1107-1114
Author(s):  
Ekta Pandey
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Szász Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

scholarly journals Approximation properties of Jain-Stancu operators

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1081-1088 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Asymptotic Expansion ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Stancu Operators ◽  
Lagrange Expansion ◽  
Preserve Linear

In the present paper, we introduce the Stancu type Jain operators, which generalize the wellknown Sz?sz-Mirakyan operators via Lagrange expansion. We investigate their weighted approximation properties and compute the error of approximation by using the modulus of continuity. We also give an asymptotic expansion of Voronovskaya type. Finally, we introduce a modified form of our operators, which preserves linear functions, provides a better error estimation than the Jain operators and allows us to give global results in a certain subclass of C[0,?). Note that the usual Jain operators do not preserve linear functions and the global results in a certain subspace of C[0,?) can not be given for them.

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 Approximation of Durrmeyer Type Operators Depending on Certain Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Neha Malik ◽  
Serkan Araci ◽  
Man Singh Beniwal
Keyword(s):  
Asymptotic Formula ◽  
Local Approximation ◽  
Approximation Properties ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators

Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper.

I-approximation properties of certain class of linear positive operators

2011 ◽  
Vol 48 (2) ◽  
pp. 205-219
Author(s):  
Nazim Mahmudov ◽  
Mehmet Özarslan ◽  
Pembe Sabancigil
Keyword(s):  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Approximation Properties ◽  
Global Approximation ◽  
Linear Positive Operators ◽  
Durrmeyer Operators

In this paper we studyI-approximation properties of certain class of linear positive operators. The two main tools used in this paper areI-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we defineq-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

scholarly journals Integral modification of Apostol-Genocchi operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2533-2544
Author(s):  
N Neha ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Absolute Error ◽  
Local Approximation ◽  
Approximation Properties ◽  
Type Space ◽  
Durrmeyer Operators ◽  
Genocchi Polynomials ◽  
The Absolute ◽  
Mathematica Software

In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study the approximation properties of these Durrmeyer operators. Furthermore, we examine the approximation behaviour of these operators including K-functional. We estimate the rate of convergence of the proposed operators for function in Lipschitz-type space and local approximation results by using modulus of continuity. Employing Mathematica software, to show the approximation and the absolute error graphically by varying the values of given parameters.

scholarly journals Approximation on bivariate parametric-extension of Baskakov-Durrmeyer-operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2783-2800
Author(s):  
Md Nasiruzzaman ◽  
Nadeem Rao ◽  
Manish Kumar ◽  
Ravi Kumar
Keyword(s):  
Modulus Of Continuity ◽  
Maximal Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Durrmeyer Operators ◽  
Mixed Modulus Of Continuity ◽  
Mixed Modulus

The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with the aid of non-negative parametric variants suppose 0 ? ?1,?2 ? 1. We obtain the order of approximation by use of the modulus of continuity in terms of well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here the approximation properties of the operators in B?gel-spaces by use of mixed-modulus of continuity.

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