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<p>We present a version of the Clarke-Ledyaev inequality that does not involve elements of the dual space. The proof relies mainly on geometry and on the classical lemma of Bishop and Phelps. In addition, this approach allows us to provide a simplified proof of the Clarke-Ledyaev inequality. The approach is primal in the sense that no dual arguments are used.</p>

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A primal approach to the Clarke-Ledyaev inequality

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Mihail Hamamdjiev,
  • Milen Ivanov,
  • Nadia Zlateva

摘要

We present a version of the Clarke-Ledyaev inequality that does not involve elements of the dual space. The proof relies mainly on geometry and on the classical lemma of Bishop and Phelps. In addition, this approach allows us to provide a simplified proof of the Clarke-Ledyaev inequality. The approach is primal in the sense that no dual arguments are used.