On Iterative Combination of Modified Bernstein-Type Polynomials

2008 ◽  
Vol 15 (4) ◽  
pp. 591-600
Author(s):  
P. N. Agrawal ◽  
Asha Ram Gairola ◽  
Vijay Gupta
Keyword(s):  
Linear Functions ◽  
Bernstein Type ◽  
Durrmeyer Operators ◽  
New Type ◽  
Direct Results

Abstract The paper deals with some direct results on ordinary and simultaneous approximations for iterative combinations of a new type of Bernstein–Durrmeyer operators. Gupta and Vasishtha [Math. Comput. Modelling 39: 521–527, 2004] have recently claimed that iterative combinations can be applied only for those operators for which 𝑡 maps exactly to 𝑥. Here we disagree with their claim and state that iterative combinations can be applied for other operators which do not reproduce linear functions either.

scholarly journals On approximation of Bernstein-Durrmeyer-type operators in movable interval

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1191-1203
Author(s):  
Fengfeng Wang ◽  
Dansheng Yu
Keyword(s):  
Asymptotic Estimate ◽  
Continuous Functions ◽  
Linear Functions ◽  
Approximation Rate ◽  
Durrmeyer Operators ◽  
New Type ◽  
Durrmeyer Type Operators

In the present paper, we introduce a new type of Bernstein-Durrmeyer operators preserving linear functions in movable interval. The approximation rate of the new operators for continuous functions and Voronovskaja?s asymptotic estimate are obtained.

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 Applications of (p,q)-gamma function to Szász Durrmeyer operators

2017 ◽  
Vol 102 (116) ◽  
pp. 211-220 ◽  
Author(s):  
Ali Aral ◽  
Vijay Gupta
Keyword(s):  
Gamma Function ◽  
Durrmeyer Operators ◽  
Direct Results

We define a (p,q) analogue of Gamma function. As an application, we propose (p,q)-Sz?sz-Durrmeyer operators, estimate moments and establish some direct results.

scholarly journals On certain q Baskakov-Durrmeyer operators

2013 ◽  
Vol 22 (1) ◽  
pp. 1-8
Author(s):  
ALI ARAL ◽  
◽  
VIJAY GUPTA ◽  
Keyword(s):  
Durrmeyer Operators ◽  
Direct Results

The present paper deals with the new q analogue of Baskakov-Durrmeyer operators. Here we estimate some direct results using the applications of q calculus.

scholarly journals Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on p , q -Integers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Exponential Function ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators ◽  
Direct Results

In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.

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

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.

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