On some class of exponential type operators

Agnieszka Tyliba, and Eugeniusz Wachnicki. "On some class of exponential type operators." Commentationes Mathematicae 45.1 (2005): null. <http://eudml.org/doc/291884>.

@article{AgnieszkaTyliba2005,
abstract = {Starting from a differential equation $\frac\{\partial \}\{\partial t\} W (\lambda , t, u)=\frac\{\lambda (u-t)\}\{p(t)\}W(\lambda ,t,u)-\beta W(\lambda ,t,u)$ for the kernel of an operator $S_\lambda (f,t) = \int _\{A\}^\{B\}W(\lambda ,t,u)f(u)du$ with the normalization condition $\int _A^B W(\lambda , t, u)du = 1$ we prove some properties which are similar to properties proved by Ismail and May for the exponential operators. In particular, we show that all these operators are approximation operators. Moreover, a method of determining $S_\lambda $ for a given function $p$ is introduced.},
author = {Agnieszka Tyliba, Eugeniusz Wachnicki},
journal = {Commentationes Mathematicae},
keywords = {exponential operators; Voronovskaya type theorem; rate of convergence; limit value problems},
language = {eng},
number = {1},
pages = {null},
title = {On some class of exponential type operators},
url = {http://eudml.org/doc/291884},
volume = {45},
year = {2005},
}

TY - JOUR
AU - Agnieszka Tyliba
AU - Eugeniusz Wachnicki
TI - On some class of exponential type operators
JO - Commentationes Mathematicae
PY - 2005
VL - 45
IS - 1
SP - null
AB - Starting from a differential equation $\frac{\partial }{\partial t} W (\lambda , t, u)=\frac{\lambda (u-t)}{p(t)}W(\lambda ,t,u)-\beta W(\lambda ,t,u)$ for the kernel of an operator $S_\lambda (f,t) = \int _{A}^{B}W(\lambda ,t,u)f(u)du$ with the normalization condition $\int _A^B W(\lambda , t, u)du = 1$ we prove some properties which are similar to properties proved by Ismail and May for the exponential operators. In particular, we show that all these operators are approximation operators. Moreover, a method of determining $S_\lambda $ for a given function $p$ is introduced.
LA - eng
KW - exponential operators; Voronovskaya type theorem; rate of convergence; limit value problems
UR - http://eudml.org/doc/291884
ER -