A Leibniz differentiation formula for positive operators |
| |
| Authors: | Chris Impens Ioan Gavrea |
| |
| Affiliation: | a Department of Pure Mathematics and Computer Algebra, University of Gent, Galglaan 2, B-9000 Gent, Belgium
b Department of Mathematics, Technical University of Cluj-Napoca, RO-3400 Cluj-Napoca, Romania |
| |
| Abstract: | Is is shown that for n→+∞ the Leibnizian combination L′n(fg)−fL′n(g)−gL′n(f) converges uniformly to zero on a compact interval W if the positive operators Ln belong to a certain class (including Bernstein, Gauss-Weierstrass and many others), and if the moduli of continuity of f,g satisfy ωW(f;h)ωW(g;h)=o(h) as h→0+. A counterexample shows that Lipschitz conditions are not appropriate to bring about a second-order version of this formula. |
| |
| Keywords: | Positive linear operator Exponential-type operator Lipschitz classes |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
