Genuine link Baskakov–Durrmeyer operators

2018 ◽  
Vol 25 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Vijay Gupta ◽  
Neha Malik
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Weighted Approximation ◽  
Approximation Result ◽  
Durrmeyer Operators ◽  
Direct Results

AbstractIn the present paper, we propose a sequence of generalized genuine Baskakov–Durrmeyer-type link operators. In terms of ordinary approximation, we estimate local and global direct results and also study the weighted approximation result. In terms of simultaneous approximation, we establish an asymptotic formula of Voronovskaja kind. In the last section, we prove convergence in{L_{p}}-norm.

scholarly journals Approximation Properties of New Modified Gamma Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yun-Shun Wu ◽  
Wen-Tao Cheng ◽  
Wei-Ping Zhou ◽  
Lun-Zhi Deng
Keyword(s):  
Asymptotic Formula ◽  
Weighted Approximation ◽  
Central Moment ◽  
Sixth Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Type Approximation ◽  
Quantitative Properties ◽  
The Moment ◽  
Direct Results

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

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 Approximation with certain genuine hybrid operators

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2335-2348
Author(s):  
Vijay Gupta ◽  
Th.M. Rassias ◽  
P.N. Agrawal ◽  
Meenu Goyal
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Integral Type ◽  
General Sequence ◽  
First Order ◽  
Error Estimations ◽  
Direct Results

In the present article, we introduce a general sequence of summation-integral type operators. We establish some direct results which include Voronovskaja type asymptotic formula, point-wise convergence for derivatives, error estimations in terms of modulus of continuity and weighted approximation for these operators. Furthermore, the convergence of these operators and their first order derivatives to certain functions and their corresponding derivatives respectively is illustrated by graphics using Matlab algorithms for some particular values of the parameters c and ?.

scholarly journals Generalized Baskakov Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6131-6151
Author(s):  
P.N. Agrawal ◽  
Meenu Goyal
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Statistical Convergence ◽  
Simultaneous Approximation ◽  
Weighted Approximation ◽  
Function Of Bounded Variation ◽  
Convergence Properties ◽  
Almost Everywhere ◽  
Direct Results ◽  
Kantorovich Operators

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operators.

scholarly journals Approximation by generalized Srivastava-Gupta operators based on certain parameter

2017 ◽  
Vol 101 (115) ◽  
pp. 247-259 ◽  
Author(s):  
D.K. Verma
Keyword(s):  
Asymptotic Formula ◽  
Error Estimate ◽  
Modulus Of Continuity ◽  
Pointwise Convergence ◽  
Simultaneous Approximation ◽  
Direct Results

We establish some direct results in simultaneous approximation for a generalization of the Srivastava-Gupta operators. We establish pointwise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of modulus of continuity of the function.

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.

Rate of Approximation for Certain Szasz–Mirakyan–Durrmeyer Operators

2009 ◽  
Vol 16 (3) ◽  
pp. 475-487
Author(s):  
Deepak Kumar Dubey ◽  
Ravindra Kumar Gangwar ◽  
Shipra Jain
Keyword(s):  
Weight Function ◽  
Basis Function ◽  
Simultaneous Approximation ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Direct Results

Abstract We study a certain integral modification of the well known Szasz–Mirakyan operators with a weight function of a general Baskakov basis function. We establish some direct results on a simultaneous approximation for these new operators.

scholarly journals New modified Baskakov operators based on the inverse Pólya-Eggenberger distribution

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3537-3550
Author(s):  
Naokant Deo ◽  
Minakshi Dhamija ◽  
Dan Miclăuş
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Present Article ◽  
Baskakov Operators ◽  
Direct Results

In the present article we introduce some modifications of the Baskakov operators in sense of the Lupa? operators based on the inverse P?lya-Eggenberger distribution. For these new modifications we derive some direct results concerning the uniform convergence and the asymptotic formula, as well as some quantitative type theorems.

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