Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1228.41019
Cárdenas-Morales, D.; Garrancho, P.; Raşa, I.
Bernstein-type operators which preserve polynomials. (English)
[J] Comput. Math. Appl. 62, No. 1, 158-163 (2011). ISSN 0898-1221

Summary: We present the sequence of linear Bernstein-type operators defined for $f\in C[0,1]$ by $B_{n}(f\deg \tau^{ - 1})\deg \tau$, $B_{n}$ being the classical Bernstein operators and $\tau $ being any function that is continuously differentiable $\infty$ times on $[0,1]$, such that $\tau (0)=0$, $\tau (1)=1$ and $\tau'(x)>0$ for $x\in [0,1]$. We investigate its shape preserving and convergence properties, as well as its asymptotic behavior and saturation. Moreover, these operators and others of King type are compared with each other and with $B_{n}$. We present as an interesting byproduct sequences of positive linear operators of polynomial type with nice geometric shape preserving properties, which converge to the identity, which in a certain sense improve $B_{n}$ in approximating a number of increasing functions, and which, apart from the constant functions, fix suitable polynomials of a prescribed degree. The notion of convexity with respect to $\tau$ plays an important role.

MSC 2000:: *41A36 Approximation by positive operators

Keywords: Bernstein-type operator; positive linear operator; Voronovskaja-type formula; generalized convexity

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]