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<p>In this paper, using important properties of uniformly convex functions, we prove several types of fundamental inequalities as Jensen, its modification Jensen-Mercer, conversion of Jensen inequality and the Hermite-Hadamard inequality for uniformly convex functions. As applications of the main results we obtain new bounds for the joint entropy as well as new estimates of the bounds involving <i>p</i>-logarithmic means and their particular cases.</p>

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Inequalities related to uniformly convex functions with applications to joint entropy and p-logarithmic means

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Yamin Sayyari,
  • Slavica Ivelić Bradanović,
  • Hasan Barsam

摘要

In this paper, using important properties of uniformly convex functions, we prove several types of fundamental inequalities as Jensen, its modification Jensen-Mercer, conversion of Jensen inequality and the Hermite-Hadamard inequality for uniformly convex functions. As applications of the main results we obtain new bounds for the joint entropy as well as new estimates of the bounds involving p-logarithmic means and their particular cases.