Bernstein–Kantorovich operators, approximation and shape preserving properties
Bernstein–Kantorovich operators, approximation and shape preserving properties
Abstract Inspired by the construction of Bernstein and Kantorovich operators, we introduce a family of positive linear operators $$\mathcal{K}_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> preserving the affine functions. Their approximation properties are investigated and compared with similar properties of other operators. We determine the central moments of all …