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

We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein polynomials by the $r$th Ditzian-Totik modulus of smoothness $ω_ϕ^{r}(f,t)_w$ where $ϕ$ is an admissible step-weight function.

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