Necessary Conditions to Obtain Voronovskaja Type Asymptotic Formulae via Statistical Limit

摘要

It is well-known that, obtaining the necessary and sufficient conditions is not an easy task in the approximation theory. In a recent paper, necessary and sufficient conditions to obtain direct and inverse results for a sequence of general positive linear operators are given by us. Our results are valid for not only uniform approximation but also statistical approximation. On the other hand, Voronovskaja obtained an asymptotic formulae to determine the order of uniform approximation of Bernstein polynomials to the function f. The main purpose of this paper is to give necessary conditions to obtain a Voronovskaja type asymptotic formulae for a sequence of general positive linear operators via statistical limit.