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Remarks on strongly convex functions

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Abstract

Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers–Ulam stability result for strongly convex functions are given. An integral Jensen-type inequality and a Hermite–Hadamard-type inequality for strongly convex functions are obtained. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is shown.

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Authors and Affiliations

  1. Escuela de Matemáticas, Universidad Central de Venezuela, Caracas, Venezuela

    Nelson Merentes

  2. Department of Mathematics and Computer Science, University of Bielsko-Biała, ul. Willowa 2, 43-309, Bielsko-Biała, Poland

    Kazimierz Nikodem

Authors
  1. Nelson Merentes
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  2. Kazimierz Nikodem
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Correspondence to Kazimierz Nikodem.

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Dedicated to Professor János Aczél on his 85th birthday

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Merentes, N., Nikodem, K. Remarks on strongly convex functions. Aequat. Math. 80, 193–199 (2010). https://doi.org/10.1007/s00010-010-0043-0

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  • DOI: https://doi.org/10.1007/s00010-010-0043-0

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