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 ,, and is a sequence of functions defined on that have the following properties for all :
  1. . Alternatively, has a Taylor series on.
  2. is completely monotone, i.e..
  3. 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.