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Chapter 3 is focused on the refinements of some more classical inequalities in continuous/family forms, but now by using the concepts of strong convexity and superquadraticity, two important notions connected to usual convexity. In particular, in this way, some refined versions of continuous forms of the following inequalities are stated, proved, and applied: Jensen’s inequality, Hermite-Hadamard’s inequality, Minkowski’s inequality, and Beckenbach-Dresher’s inequality.

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Refinements of Inequalities via Strong Convexity and Superquadracity

  • 章节

  • 发表日期：

    2025年

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

摘要

Chapter 3 is focused on the refinements of some more classical inequalities in continuous/family forms, but now by using the concepts of strong convexity and superquadraticity, two important notions connected to usual convexity. In particular, in this way, some refined versions of continuous forms of the following inequalities are stated, proved, and applied: Jensen’s inequality, Hermite-Hadamard’s inequality, Minkowski’s inequality, and Beckenbach-Dresher’s inequality.