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<p>The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider Hölder-, Minkowski-, and Jensen-type inequalities. Generalized quasi-arithmetic means are defined by taking strictly monotone generating functions instead of strictly monotone and continuous ones.</p>

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Hölder- and Minkowski-type inequalities for generalized quasi-arithmetic means

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Zsolt Páles,
  • Paweł Pasteczka

摘要

The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider Hölder-, Minkowski-, and Jensen-type inequalities. Generalized quasi-arithmetic means are defined by taking strictly monotone generating functions instead of strictly monotone and continuous ones.