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Remarks on a Lemma of Schmidt

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Abstract

Inspired by a lemma of Schmidt (Proc Am Math Soc 124:3003–3013, 1996) we present several inequalities involving

$$\begin{aligned}{} & {} \max _{1\le j\le n} |1-x_j|, \quad \max _{1\le j \le n} |\log ( x_j)| \quad \text{ and } \quad \left( \sum _{i=1}^n |1-x_i|^r \right) ^{1/r},\\ {}{} & {} \quad \left( \sum _{i=1}^n |\log ( x_i)|^r \right) ^{1/r}. \end{aligned}$$

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Authors and Affiliations

  1. Morsbacher Straße 10, 51545, Waldbröl, Germany

    Horst Alzer

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Hong Kong

    Man Kam Kwong

  3. Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului Street 28, 400114, Cluj-Napoca, Romania

    Ioan Raşa

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  1. Horst Alzer
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  2. Man Kam Kwong
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  3. Ioan Raşa
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Correspondence to Horst Alzer.

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Alzer, H., Kwong, M.K. & Raşa, I. Remarks on a Lemma of Schmidt. Results Math 78, 216 (2023). https://doi.org/10.1007/s00025-023-01990-8

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