IJPAM: Volume 44, No. 1 (2008)

APPROXIMATION PROPERTIES OF CERTAIN
NONLINEAR SUMMATION OPERATORS

Lucyna Rempulska$^1$, Agnieszka Thiel$^2$
$^{1,2}$Institute of Mathematics
Poznan University of Technology
ul. Piotrowo 3a, Poznan, 60-965, POLAND
$^1$e-mail: lrempuls@math.put.poznan.pl
$^2$e-mail: athiel@interia.pl


Abstract.We investigate a class of nonlinear summation operators $L_n^*$ defined by a modification of some positive linear operators $L_n$ in polynomial weighted spaces. The operators $L_{n;r}$ and $L_{n;r}^*$ for $r$-times defferentiable functions will be examined also.

We give direct approximation theorems for considered operators.

Received: January 26, 2008

AMS Subject Classification: 41A25, 41A36

Key Words and Phrases: linear operator, nonlinear operator, polynomial weighted space, degree of approximation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 1