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<p>For each integer <i>n</i> at least 3 and real number <i>c</i>, we construct an <i>n</i> − 1 times Peano differentiable function at <i>c</i> with the property that it is <i>n</i> times Riemann differentiable at <i>c</i>, but not <i>n</i> times Peano differentiable at <i>c</i>.</p>

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Nonequivalence between Peano and Riemann derivatives

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Stefan Catoiu,
  • Hajrudin Fejzić

摘要

For each integer n at least 3 and real number c, we construct an n − 1 times Peano differentiable function at c with the property that it is n times Riemann differentiable at c, but not n times Peano differentiable at c.