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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 808.41006

**Autor: ** Erdös, Paul; Newman, D.J.; Knappenberger, J.

**Title: ** Forcing two sums simultaneously. (In English)

**Source: ** Knopp, Marvin (ed.) et al., A tribute to Emil Grosswald: number theory and related analysis. Providence, RI: American Mathematical Society, Contemp. Math. 143, 321-328 (1993).

**Review: ** The second author and *T. J. Rivlin* [Analysis 3, 355-367 (1983; Zbl 575.41006)] sought an optimal rational interpolation process that was Féjer-stable at all sets of nodes \bf x: (x_{0},..., x_{n}). They established the proposition that, if \bf x in (0,n] and n \geq 2, then **max**_{y in (0,n]} \left**{****[****sum**^{n}_{k = 1} 1/|y-x_{k}|**]** / **[****sum**^{n}_{k = 1} 1/(y- x_{k})^{2}**]**\right**}** \geq (log n)/300. In this paper, the authors strengthen this result by showing that when n is large, there is a point y in [0,n] where the numerator exceeds a constant times log n and the denominator is bounded.

**Reviewer: ** P.A.McCoy (Annapolis)

**Classif.: ** * 41A17 Inequalities in approximation

26D05 Inequalities for trigonometric functions and polynomials

26D15 Inequalities for sums, series and integrals of real functions

**Keywords: ** Fejer-stable interpolation; asymptotic lower bound

**Citations: ** Zbl 575.41006

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