Some Good Sequences of Interpolatory Polynomials

Abstract

In 1963, P. L. Butzer [4, p. 180] asked whether it was possible to prove Jackson's theorem by means of an operator which is "almost" interpolatory in the sense that it is based on the values of the approximee at a finite number of nodes. In answer to this question, G. Freud introduced [4] a sequence of operators which led to an independent proof of Jackson's theorem. Strictly speaking these operators are not interpolatory but they are "almost" interpolatory in the above sense.