Abstract
The problem attacked here is to find smaller factors? (n,?),n > ?, for the inequality $$\delta _n [f] \leqq \gamma (n,\varrho ) \cdot \mathop {\sup }\limits_{x \in [ - 1,1]} |f^{(\varrho )} (x)|$$ than are already known. Heref(? (x) denotes the?-th derivative off(x), and? n [f] is the error of the best Chebyshev-approximation off by algebraic polynomials of degree ?n. A new approach to this problem is demonstrated and the results we got forn?9,??8 by the use of a computer are presented.
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