Baskakov operator

In functional analysis, a branch of mathematics, the Baskakov operators are generalizations of Bernstein polynomials, Szász–Mirakyan operators, and Lupas operators. They are defined by

where ( can be ), , and is a sequence of functions defined on that have the following properties for all :

1. . Alternatively, has a Taylor series on .
3. is completely monotone, i.e. .
4. There is an integer such that whenever

They are named after V. A. Baskakov, who studied their convergence to bounded, continuous functions.

Basic results

The Baskakov operators are linear and positive.

References

Footnotes