On a theorem of Jackson
Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 681-690
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We prove that $$ \inf_{L_n\in Z_n}\sup_\omega\,^*\sup_{f\in H_\omega}\frac{\|f-L_n(f)\|}{\omega(\frac\pi{n+1})}=1\quad(n=0,1,2,\dots), $$ where $\inf\limits_{L_n\in Z_n}$ is taken over all linear polynomial approximation methods of degree not higher than $n$ and $\sup\limits_\omega{}^*$ over all convex moduli of continuity $\omega(\delta)$.