Approximation of Functions on [−1,1] and Their Derivatives by Polynomial Projection Operators

Pointwise estimates are obtained for the simultaneous approximation of a function f ?C^q-1,1] and its derivatives f⁽¹⁾, …, f^(q) by means of an arbitrary sequence of bounded linear projection operators L_n which map C-1,1] into the polynomials of degree at most n, augmented by the interpolation of f at some points near ± 1.