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About Karamata Mean Value Theorem, Some Consequences and Some Stability Results

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Abstract

The aim of this paper is to explore Karamata’s mean value theorem. In the second section, we reformulate a mean theorem for the convex functions and prove some consequences. Also, we prove an integral version of Karamta theorem. Third section is reserved to the stability results. We establish some conditions for the stability of the intermediate point arising from Karamata, Godner and the integral mean theorem proved in the previous section.

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Authors and Affiliations

  1. Iancu de Hunedoara National College, Str. Victoriei, nr. 12, 331057, Hunedoara, Romania

    Dan Ştefan Marinescu

  2. University Politehnica of Bucharest, Bd. Splaiul Independenţei, nr. 313, 060042, Bucharest, Romania

    Mihai Monea & Cristinel Mortici

  3. Decebal National College, Str. 1 Decembrie 1918, nr. 22, 330025, Deva, Romania

    Mihai Monea

  4. Valahia University of Târgovişte, Bd. Unirii, nr. 18, 130082, Târgovişte, Romania

    Cristinel Mortici

  5. Academy of Romanian Scientists, Bd. Splaiul Independenţei, nr. 54, 050094, Bucharest, Romania

    Cristinel Mortici

Authors
  1. Dan Ştefan Marinescu
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  2. Mihai Monea
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  3. Cristinel Mortici
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Correspondence to Mihai Monea.

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Marinescu, D.Ş., Monea, M. & Mortici, C. About Karamata Mean Value Theorem, Some Consequences and Some Stability Results. Results Math 72, 329–342 (2017). https://doi.org/10.1007/s00025-017-0680-x

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  • DOI: https://doi.org/10.1007/s00025-017-0680-x

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