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Inequalities Due to T. S. Nanjundiah

  • P. S. Bullen
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

In this note we give Nanjundiah’s proofs of his mixed geometric-arithmetic mean inequalities; in particular his use of inverse means is explained.

Key words and phrases

Geometric-arithmetic mean inequalities Inverse means Mixed mean inequality Carleman’s inequality Rado’s inequality Popoviciu’s inequality Hölder’s inequality, Čebišev’s inequality, Sequence of the power means 

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References

  1. 1.
    P. S. Bullen, D. S. Mitrinović and P. M. Vasić, Means and Their Inequalities, Reidel Publishing Co., Dordrecht — Boston, 1988.zbMATHGoogle Scholar
  2. 2.
    K. Kedlaya Proof of a mixed arithmetic-mean geometric-mean inequality, Amer. Math. Monthly 101 (1954), 355–357.MathSciNetCrossRefGoogle Scholar
  3. 3.
    T. Matsuda An inductive proof of a mixed arithmetic-geometric mean inequality, Amer. Math. Monthly 102 (1955), 634–637.MathSciNetCrossRefGoogle Scholar
  4. 4.
    T. S. Nanjundiah, Inequalities relating to arithmetic and geometric means I, II, J. Mysore Univ. Sect. B6 (1946), 63–77 and 107-113.MathSciNetGoogle Scholar
  5. 5.
    T. S. Nanjundiah, Sharpening some classical inequalities, Math. Student 20 (1952), 24–25.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • P. S. Bullen
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouver BCCanada

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