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

2010/08/09 by Wen-ming Lu, Wen-Ming Lu, Lin Zhang +2
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #math.FA

paper · pdf · doi:10.48550/arxiv.1008.1439

10 pages, latex

openalex publication_date 2010/08/09 · arxiv created 2010/08/26 · arxiv updated 2010/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_ϕ^r(f,t)_w where ϕ is an admissible step-weight function.

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