We prove an identity for basis functions of a general family of positive linear operators. It covers as special cases the Bernstein, Szász–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 Stöckler. As an application we give...

Using the family of generalized Baskakov operators we propose a general method to construct positive linear preserving exponential functions. A conjecture concerning Voronovskaja type formula and some applications are presented.

We present two general sequences of positive linear operators. The first is introduced by using a class of dependent random variables, and the second is a mixture between two linear operators of discrete type. Our goal is to study their statistical convergence to the approximated function. This type of convergence can replace classical results provided by Bohman-Korovkin theorem. A particular c...