Convex Functions and Some Classical Inequalities

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Part of the Springer Series in Statistics book series (SSS)


Convex functions arise in a variety of contexts and are basic to a number of results. For more extensive discussions of convexity, see Roberts and Varberg (1973), Rockafeller (1970), Stoer and Witzgall (1970), van Tiel (1984), Pecărić, Proschan, and Tong (1992), Webster (1994), or Niculescu and Persson (2006). The book by Pachpatte (2005, Chapter 1) provides a compendium of inequalities involving convex functions.


Convex Function Full Rank Hermitian Matrice Classical Inequality Nonnegative Random Variable 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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