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Some continuous forms of the Hölder, Minkowski, Beckenbach-Dresher, Popoviciu and Bellman inequalities are stated and proved. Moreover, a close relation between the Hölder and Minkowski inequalities on these continuous/family forms is proved, namely that they are in a sense equivalent. Also, a connection to the Gauss-Pólya inequality is pointed out.

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Continuous Forms of Classical Inequalities

  • 章节

  • 发表日期：

    2025年

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  • Ludmila Nikolova,
  • Lars-Erik Persson,
  • Sanja Varošanec

摘要

Some continuous forms of the Hölder, Minkowski, Beckenbach-Dresher, Popoviciu and Bellman inequalities are stated and proved. Moreover, a close relation between the Hölder and Minkowski inequalities on these continuous/family forms is proved, namely that they are in a sense equivalent. Also, a connection to the Gauss-Pólya inequality is pointed out.