Abstract
In this note, Mahler gives new proofs for two inequalities of polynomials due to N. I. Feldman and A. O. Gelfond, respectively; these inequalities are of importance in the theory of transcendental numbers. While the original proofs by the two authors are quite unconnected, Mahler deduces both results from the same source, namely from Jensen's integral formula in the theory of analytic functions. Reprint of the author's paper \[Mathematika 7, 98--100 (1960; Zbl 0099.25003)].
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