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<p>In this paper we obtain a general method that allows to prove inequalities for convex functions. In fact, we show that proving an inequality for every convex function is equivalent to proving that inequality for a small class of simple convex functions. Also, we show the power of this tool by proving several results: Jensen’s inequality, an integral version of the Petrović’s inequality, two new integral Karamata’s inequality, and a new version of Hermite-Hadamard inequality with general measures.</p>

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A Reduction Theorem for Inequalities Involving Convex Functions and Its Applications

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • José M. Rodríguez,
  • José M. Sigarreta

摘要

In this paper we obtain a general method that allows to prove inequalities for convex functions. In fact, we show that proving an inequality for every convex function is equivalent to proving that inequality for a small class of simple convex functions. Also, we show the power of this tool by proving several results: Jensen’s inequality, an integral version of the Petrović’s inequality, two new integral Karamata’s inequality, and a new version of Hermite-Hadamard inequality with general measures.