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.

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 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.

Rate of Approximation for Certain Durrmeyer Operators

2006 ◽  
Vol 13 (2) ◽  
pp. 277-284 ◽  
Author(s):  
Vijay Gupta ◽  
Tengiz Shervashidze ◽  
Maria Craciun
Keyword(s):  
Rate Of Convergence ◽  
Simultaneous Approximation ◽  
Present Note ◽  
Bernstein Polynomials ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Type Integral

Abstract In the present note, we study a certain Durrmeyer type integral modification of Bernstein polynomials. We investigate simultaneous approximation and estimate the rate of convergence in simultaneous approximation.

scholarly journals Rate of Convergence for Ibragimov-Gadjiev-Durrmeyer Operators

2017 ◽  
Vol 50 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Durrmeyer Operators ◽  
Special Cases ◽  
Derivatives Of

Abstract The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

scholarly journals Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Gancho Tachev
Keyword(s):  
Continuous Functions ◽  
Approximation Properties ◽  
Linear Combinations ◽  
Direct Estimate ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Phillips Operators ◽  
Bounded Continuous Functions

AbstractWe study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász-Mirakjan-Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions f E C[0,x), measured in C|\[0,x)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author-[10, 11]

Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

2012 ◽  
Vol 49 (2) ◽  
pp. 254-268
Author(s):  
Tiberiu Trif
Keyword(s):  
Rate Of Convergence ◽  
Finite Type ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Durrmeyer Operators

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

scholarly journals Lupaş-Durrmeyer operators based on Polya distribution

2014 ◽  
Vol 8 (2) ◽  
pp. 146-155 ◽  
Author(s):  
Vijay Gupta ◽  
Themistocles M. Rassias
Keyword(s):  
Durrmeyer Operators ◽  
Polya Distribution
Sign in / Sign up

Export Citation Format

Share Document