Orador Convidado: Ana Maria Acu, Department of Mathematics and Informatics, Lucian Blaga University of Sibiu

Resumo:

The research results presented here are concerned with the approximation by certain classes of  positive linear  operators. In the first part of this presentation we are interested in how non-multiplicative can a linear functional be. In order to give an answer to this question, we considered the generalized Chebyshev functional
T_{L}(f,g):=L(fcdot g)-L(f)cdot L(g),
for a positive linear functional $L$ and we obtained the estimates as follows
|T_{L}(f,g)|leq {mathcal E}(L,f,g).
These inequalities have been applied in the case of known operators. The estimates for the differences of positive linear operators is another topic which  will be presented. The results obtained are motivated by the recent results which give a solution to a problem proposed by A. Lupac s in [1]. One of the questions raised by him was to give an estimate for
B_ncirc overline{mathbb B}_n-overline{mathbb B}_ncirc B_n=: U_n-S_n,
where Bn are the Bernstein operators and Bn are the Beta operators.

References
[1] A. Lupac s, The approximation by means of some linear positive operators, in Approximation Theory (M.W. M" uller et al., eds), Akademie-Verlag, Berlin, 1995, 201-227.

Resumo (pdf):
Em anexo.