The Genuine Bernstein-Durrmeyer Operator on a Simplex

1994 ◽  
Vol 26 (1-2) ◽  
pp. 99-130 ◽  
Author(s):  
Thomas Sauer
Keyword(s):  
Durrmeyer Operator

Quantitative estimates for a new complex Durrmeyer operator in compact disks

2011 ◽  
Vol 218 (6) ◽  
pp. 2944-2951 ◽  
Author(s):  
Sorin G. Gal ◽  
Vijay Gupta
Keyword(s):  
Quantitative Estimates ◽  
Durrmeyer Operator ◽  
Compact Disks

scholarly journals Strong Converse Inequality for the Bernstein-Durrmeyer Operator

1993 ◽  
Vol 75 (1) ◽  
pp. 25-43 ◽  
Author(s):  
W. Chen ◽  
Z. Ditzian ◽  
K. Ivanov
Keyword(s):  
Durrmeyer Operator ◽  
Strong Converse Inequality ◽  
Strong Converse ◽  
Converse Inequality

scholarly journals Better approximation of functions by genuine Bernstein-Durrmeyer type operators

2019 ◽  
Vol 35 (2) ◽  
pp. 125-136
Author(s):  
ANA MARIA ACU ◽  
P. N. AGRAWAL ◽  
◽  
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Of Functions ◽  
Numerical Examples ◽  
Durrmeyer Operator ◽  
Durrmeyer Type Operators ◽  
Theoretical Results ◽  
Second Modulus Of Continuity

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.

scholarly journals A Study on the Rate of Convergence of Chlodovsky-Durrmeyer Operator and Their Bézier Variant

2017 ◽  
Vol 13 (02) ◽  
pp. 01-08
Author(s):  
S. K. Tiwari ◽  
V.K. Gupta ◽  
Yogita Parmar
Keyword(s):  
Rate Of Convergence ◽  
Durrmeyer Operator ◽  
Bézier Variant

scholarly journals Approximation Properties of a Certain Modification of  Durrmeyer Operators

2021 ◽  
Author(s):  
Asha Ram Gairola ◽  
Karunesh Kumar Singh ◽  
Hassan Khosravian Arab ◽  
Vishnu Narayan Mishra
Keyword(s):  
Error Estimate ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Durrmeyer Operators ◽  
Integrable Functions ◽  
Durrmeyer Operator ◽  
Bézier Variant

Abstract We study approximation properties of a new operator DM,1 n (f, x) introduced by Acu et al. in [Results Math 74:90, (2019)] for Lebesgue integrable functions in [0,1]. An error estimate by the Bezier variant of the operators DM,1 n (f, x)is also obtained for the functions of bounded variation. By relevant numerical examples, the orders of approximation by the operator DM,1 n (f, x) and the modified-Bernstein-Durrmeyer operator are also compared.

scholarly journals Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators

2017 ◽  
Vol 33 (1) ◽  
pp. 49-58
Author(s):  
SORIN G. GAL ◽  
◽  
SORIN TRIFA ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Pointwise Approximation ◽  
Dimensional Simplex ◽  
Set Functions ◽  
Quantitative Estimates ◽  
Durrmeyer Operator ◽  
Choquet Integrals

For the qualitative results of uniform and pointwise approximation obtained in [8], we present here general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x, written in terms of Choquet integrals with respect to a family of monotone and submodular set functions, Γn,x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

Approximation by the Bernstein–Durrmeyer Operator on a Simplex

2008 ◽  
Vol 31 (3) ◽  
pp. 289-308 ◽  
Author(s):  
Feng Dai ◽  
Hongwei Huang ◽  
Kunyang Wang
Keyword(s):  
Durrmeyer Operator

scholarly journals Approximation by Multivariate Baskakov-Durrmeyer Operator

2011 ◽  
Vol 2011 (1) ◽  
pp. 158219
Author(s):  
Feilong Cao ◽  
Yongfeng An
Keyword(s):  
Durrmeyer Operator
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