An identity for a general class of approximation operators
We prove an identity for basis functions of a general family of positive linear operators. It covers as special cases the Bernstein, Szasz Mirakjan and Baskakov operators. A corollary of our result can be considered a pointwise orthogonality relation. The Bernstein case is the univariate case of a remarkable identity which recently was presented by Jetter and Stockler. As an application we give a representation of a restricted dual basis and define a class of quasi interpolants.
J. Approx. Theory