Heinz H. Gonska

GLOBAL SMOOTHNESS OF APPROXIMATING FUNCTIONS

AMS 1980 Subject Classification (1985 Revision): 41A17, 26A15, 26A16

A test function theorem and apporoximation by pseudopolynomials

We prove a Korovkin-type theorem on approximation of bivariate functions in the space of B -continuous functions (introduced by K. Bogel in 1934). As consequences, some sequences of uniformly approximating pseudopolynomials are obtained.

Approximation theorems for the iterated Boolean sums of Bernstein operators

Abstract For the iterated Boolean sums of Bernstein operators we prove global direct, inverse and saturation results.

Quantitative theorems on approximation by Bernstein-Stancu operators

AbstractIn 1972 D. D. Stancu introduced a generalization

Approximation by Boolean sums of positive linear operators. III: Estimates for some numerical approximation schemes

L_{mp} ^{< \alpha \beta \gamma > }

ON APPROXIMATION OF CONTINUOUSLY DIFFERENTIABLE FUNCTIONS BY POSITIVE LINEAR OPERATORS

of the classical Bernstein operators given by the formula

(0,\dots,R-2,R)

L_{mp}< \alpha \beta \gamma > (f,x) = \sum\limits_{k = 0}^{m + p} {\left( {\begin{array}{*{20}c} {m + p} \\ k \\ \end{array} } \right)} \frac{{x^{(k, - \alpha )} \cdot (1 - x)^{(m + p - k, - \alpha )} }}{{1^{(m + p, - \alpha )} }}f\left( {\frac{{k + \beta }}{{m + \gamma }}} \right)