On iterative combination of Bernstein-Durrmeyer polynomials

2007 ◽  
Vol 1 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Agrawal P.N. ◽  
Gairola Ram
Keyword(s):  
Durrmeyer Polynomials

scholarly journals q-generalized Bernstein-Durrmeyer polynomials

2020 ◽  
pp. 211-235
Author(s):  
P. N. Agrawal ◽  
Ana-Maria Acu ◽  
R. Ruchi
Keyword(s):  
Durrmeyer Polynomials

scholarly journals Approximation by Genuineq-Bernstein-Durrmeyer Polynomials in Compact Disks in the Caseq>1

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Open Problem ◽  
Analytic Functions ◽  
Type Theorem ◽  
Linear Operators ◽  
Explicit Formulas ◽  
Rate Of Approximation ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

This paper deals with approximating properties of the newly definedq-generalization of the genuine Bernstein-Durrmeyer polynomials in the caseq>1, which are no longer positive linear operators onC0,1. Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuineq-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that, for functions analytic inz∈ℂ:z<R,R>q, the rate of approximation by the genuineq-Bernstein-Durrmeyer polynomialsq>1is of orderq−nversus1/nfor the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuineq-Bernstein-Durrmeyer forq>1. This paper represents an answer to the open problem initiated by Gal in (2013, page 115).

scholarly journals Bernstein-Durrmeyer polynomials on a simplex

1992 ◽  
Vol 68 (3) ◽  
pp. 247-261 ◽  
Author(s):  
H Berens ◽  
H.J Schmid ◽  
Y Xu
Keyword(s):  
Durrmeyer Polynomials

Approximation by complex summation-integral type operator in compact disks

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Vijay Gupta ◽  
Rani Yadav
Keyword(s):  
Complex Plane ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Type Operator ◽  
Approximation Properties ◽  
Integral Type ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

AbstractIn the present paper we estimate a Voronovskaja type quantitative estimate for a certain type of complex Durrmeyer polynomials, which is different from those studied previously in the literature. Such estimation is in terms of analytic functions in the compact disks. In this way, we present the evidence of overconvergence phenomenon for this type of Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. In the end, we mention certain applications.

Estimation of the quantile function using Bernstein–Durrmeyer polynomials

2013 ◽  
Vol 26 (1) ◽  
pp. 1-20 ◽  
Author(s):  
A. Pepelyshev ◽  
E. Rafajłowicz ◽  
A. Steland
Keyword(s):  
Quantile Function ◽  
Durrmeyer Polynomials

scholarly journals On Lp-Approximation by Iterative Combination of Bernstein-Durrmeyer Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
T. A. K. Sinha ◽  
P. N. Agrawal ◽  
Asha Ram Gairola
Keyword(s):  
Error Estimate ◽  
Order Approximation ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Lp Approximation ◽  
Durrmeyer Polynomials

We improve the degree of approximation by Bernstein-Durrmeyer polynomials taking their iterates and obtain error estimate in higher-order approximation.

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