AbstractPointwise estimates are obtained for simultaneous approximation of a functionfand its derivatives by means of an arbitrary sequence of bounded projection operators with some extra condition (1.3) (we do not require the operators to be linear) which mapC‐1,1into polynomials of degreen, augmented by the interpolation offat some points near ±1. The present result essentially improved those in BaKi3, and several applications are discussed in Section
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