Baskakov operator
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 
:
They are named after V. A. Baskakov, who studied their convergence to bounded, continuous functions.
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, a branch of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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 seriesTaylor seriesIn mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
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.