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Aequationes mathematicae

, Volume 80, Issue 1–2, pp 193–199 | Cite as

Remarks on strongly convex functions

  • Nelson Merentes
  • Kazimierz NikodemEmail author
Article

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.

Mathematics Subject Classification (2000)

Primary 26A51 Secondary 39B62 

Keywords

Strongly convex functions generalized convex functions Jensen inequality Hermite–Hadamard inequality 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Escuela de MatemáticasUniversidad Central de VenezuelaCaracasVenezuela
  2. 2.Department of Mathematics and Computer ScienceUniversity of Bielsko-BiałaBielsko-BiałaPoland

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