Variation on Butzer's problem: Characterization of the solutions

AbstractThe so-called Butzer problem had been a challenge to the approximation community for decades until its first constructive solution was given by Cao and Gonska at the end of the 1980s. Butzer's original problem can be turned into a “strong form”, namely a pointwise one. In the present note, we characterize, among other things, and in an easy way, certain operators which solve Butzer's problem in this strong and most demanding version

Positive linear operators with equidistant nodes

AbstractIn the present paper, the approximation power of positive linear operators with equidistant nodes is investigated. New pointwise estimates are given in terms of first and second order moduli of continuity, showing that for positive operators having uniform Jackson orders of approximation one may expect interpolation at the endopoints. In particular, the first solution to Butzer's problem with equidistant nodes is given. A negative result yields an explanation why Bernstein operators and some of their modifications are optimal in a certain sense

Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods

Quantitative approximation in C(X)

SIGLETIB: RO 1945 (94) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Degree of approximation by lacunary interpolators (0,...,R-2,R) interpolation

Present paper is the extended version of an invited lecture given at the International Conference on Constructive Function Theory, Edmonton/Canada, July 22-26, 1986SIGLETIB: RO 1945 (100) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On Almost-Hermite-Fejer-Interpolation Pointwise estimates

To appear in: Bulletin of the Australian Mathematical SocietySIGLETIB: RO 1945 (16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On Picugov-Lehnhoff operators

SIGLETIB: RO 1945 (86) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman