From Wikipedia, the free encyclopedia
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 :
- . Alternatively, has a Taylor series on .
- is completely monotone, i.e. .
- There is an integer such that whenever
They are named after V. A. Baskakov, who studied their convergence to bounded, continuous functions.[1]
The Baskakov operators are linear and positive.[2]
- Lua error in Module:Citation/CS1/Configuration at line 2083: attempt to index a boolean value.
- ^ Lua error in Module:Citation/CS1/Configuration at line 2083: attempt to index a boolean value.
- ^ Lua error in Module:Citation/CS1/Configuration at line 2083: attempt to index a boolean value.