Pacific Journal of Mathematics

Generalized convex inequalities.

Samuel Karlin and Albert Novikoff

Article information

Source
Pacific J. Math., Volume 13, Number 4 (1963), 1251-1279.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103034561

Mathematical Reviews number (MathSciNet)
MR0156927

Zentralblatt MATH identifier
0126.28102

Subjects
Primary: 26.70

Citation

Karlin, Samuel; Novikoff, Albert. Generalized convex inequalities. Pacific J. Math. 13 (1963), no. 4, 1251--1279. https://projecteuclid.org/euclid.pjm/1103034561


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References

  • [1] E. F. Beckenbach, and R. Bellman, Inequalities, Ergebnisse der Math, und Ihrer Grenzgebiete, Neue Folge, Heft 30, Springer-Verlag, 1961.
  • [2] G. H. Hardy, J. E. Littlewood and G. Plya, Inequalities, Cambridge University Press, 2nd Ed., 1952.
  • [3] G. H. Hardy,Some simple inequalities satisfied by convex functions, Mess. Math., 58 (1929), 145-152.
  • [4] E. Hoeffding, On the distribution of the number of successes in independenttrials, Annals Math. Stat., 27, No. 3 (1956),713-721.
  • [5] S. Karlin, Total Positivity and Applications, a forthcoming book.
  • [6] S. Karlin, F. Proschan, and R. Barlow, Moment inequalities of Plya frequency func- tions, Pacific J. Math., 11, No. 3 (1961), 1023-1033.
  • [7] S. Karlin, Total Positivity and Convexity PreservingTransformations,Proc. of Symposia in Pure Math. Vol. VII, Convexity. Amer. Math. Soc, 1963.
  • [8] S. Karlin, and H. Rubin, The theory of decision procedures for distributionswith monotone likelihood ratio, Ann. Math. Stat., 27 (1956), 272-299.
  • [9] L. Mirsky, On the trace of matrix products, Mathematische Nachrichten (1959), 161-174.
  • [10] G. Plya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc, 24 (1922), 312-324.
  • [11] I. J. Schoenberg, On Plya frequency functions, I, J. d'Analyse Math., I (1951), 331- 374.