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Anti-L’Hôpital Differentiable Functions

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Abstract

Large algebraic structures are found inside the family of those real differentiable functions f on the real line having the property that, for a prescribed subset Z, the continuity of \(f'\) fails at the points of Z, so showing that, even in the easiest case, the L’Hôpital rule should be used carefully.

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Authors and Affiliations

  1. Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41080, Seville, Spain

    Luis Bernal-González & María del Carmen Calderón-Moreno

Authors
  1. Luis Bernal-González
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  2. María del Carmen Calderón-Moreno
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Correspondence to María del Carmen Calderón-Moreno.

Additional information

The authors have been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1P.

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Bernal-González, L., Calderón-Moreno, M.d.C. Anti-L’Hôpital Differentiable Functions. Mediterr. J. Math. 14, 8 (2017). https://doi.org/10.1007/s00009-016-0807-4

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  • DOI: https://doi.org/10.1007/s00009-016-0807-4

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