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).

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.

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 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 Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

2021 ◽  
pp. 1666-1674
Author(s):  
Ali J. Mohammad ◽  
Amal K. Hassan
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Linear Operators ◽  
Order Of Approximation ◽  
Integral Type ◽  
Test Function ◽  
Numerical Example ◽  
First Derivative ◽  
Two Parameters

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters. 

scholarly journals Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1517-1530 ◽  
Author(s):  
M. Mursaleen ◽  
Shagufta Rahman ◽  
Khursheed Ansari
Keyword(s):  
Upper Bound ◽  
Simultaneous Approximation ◽  
Approximation Theorem ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators

In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bound for the approximation to rth derivative of a function by these operators is established. Furthermore, we obtain A-statistical approximation properties of these operators with the help of universal korovkin type statistical approximation theorem.

On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant

2009 ◽  
Vol 16 (4) ◽  
pp. 693-704
Author(s):  
Harun Karsli ◽  
Paulina Pych-Taberska
Keyword(s):  
Recent Result ◽  
Pointwise Convergence ◽  
Rates Of Convergence ◽  
Durrmeyer Operators ◽  
The One ◽  
Special Case ◽  
Appl Math ◽  
Bézier Variant

Abstract We consider the Bézier variant of Chlodovsky–Durrmeyer operators 𝐷𝑛,α for functions 𝑓 measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (𝐷𝑛,α 𝑓) (𝑥) at those 𝑥 > 0 at which the one-sided limits 𝑓(𝑥+), 𝑓(𝑥–) exist. In the special case α = 1 the recent result of [Ibikli, Karsli, J. Inequal. Pure Appl. Math. 6: 12, 2005] concerning the Chlodovsky–Durrmeyer operators 𝐷𝑛 is essentially improved and extended to more general classes of functions.

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