A unified approach to uniform real approximation by polynomials with linear restrictions

Abstract

Problems concerning approximation of real-valued continuous functions of a real variable by polynomials of degree smaller than n with various linear restrictions have been studied by several authors. This paper is an attempt to provide a unified approach to these problems. In particular, the notion of restricted derivatives approximation is seen to fit into the theory and includes as special cases the notions of monotone approximation and restricted range approximation. Also bounded coefficients approximation, ε \varepsilon -interpolator approximation, and polynomial approximation with interpolation fit into our scheme.