Direct and Inverse Estimates for Combinations of Bernstein Polynomials with Endpoint Singularities

Lu Wenming

Lu Wenming School of Science, Hangzhou Dianzi Unviersity, Hangzhou, 310018 P.R. China

Keywords: Bernstein polynomials, Endpoint singularities, Pointwise approximation, Direct and inverse theorems.

Abstract

We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness ω r φ (f, t)w where φ is an admissible step-weight function.

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