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Asymptotic Approximation by Bernstein-Durrmeyer Operators and their Derivatives
(Technische Hochschule Mittelhessen; Gießen, 2000)
The concern of this paper is the study of local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. ...
Asymptotic Expansion of the Multivariate Bernstein Polynomials on a Simplex
(Technische Hochschule Mittelhessen; Gießen, 2000)
In this note we study the local behaviour of the multi-variate Bernstein polynomials on a d-dimensional simplex S. For functions f admitting derivatives of sufficient high order in a point x of S we derive the complete ...
The Asymptotic Expansion for Approximation Operators of Favard-Szász Type
(Technische Hochschule Mittelhessen; Gießen, 1999)
We derive the complete asymptotic expansion for Favard-Szász type operators introduced
by Jakimovski and Leviatan. Furthermore, we treat simultaneous approximation.