Positive and Copositive Spline Approximation in L P 0; 1]

Abstract

The order of positive and copositive spline approximation in the L p-norm, 1 p < 1, is studied, the main results are (1) the error of positive approximation by splines is bounded by C! 2 (f; 1=n) p if f has a nonnegative extension; (2) the order deteriorates to ! 1 if f does not have such an extension; (3) the error of copositive spline approximation is… (More)

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