Geodesic
On some class of exponential type operators
Commentationes Mathematicae, Tome 45 (2005) no. 1, pp. 57-70.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/cm.v45i1.5228
Mots-clés : exponential operators, Voronovskaya type theorem, rate of convergence, limit value problems 
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Agnieszka Tyliba; Eugeniusz Wachnicki. On some class of exponential type operators. Commentationes Mathematicae, Tome 45 (2005) no. 1, pp.  57-70. doi : 10.14708/cm.v45i1.5228. http://geodesic.mathdoc.fr/articles/10.14708/cm.v45i1.5228/

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