Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On extensions of an inequality among means

Authors: F. Chan, D. Goldberg and S. Gonek
Journal: Proc. Amer. Math. Soc. 42 (1974), 202-207
MSC: Primary 26A86
MathSciNet review: 0338295
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An inequality of Fan relates the arithmetic and geometric means of x and $ 1 - x$. An extension to generalized means is conjectured. This conjecture is proven for several special cases. In addition, some counterexamples are given.

References [Enhancements On Off] (What's this?)

  • [1] E. F. Beckenbach and R. Bellman, Inequalities, 2nd ed., Ergebnisse der Math. und ihrer Grenzgebiete, Band 30, Springer-Verlag, New York, 1965, p. 5. MR 33 #236. MR 0192009 (33:236)
  • [2] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, New York, 1952. MR 13, 727. MR 0046395 (13:727e)
  • [3] S. Lawrence and D. Segalman, A generalization of two inequalities involving means, Proc. Amer. Math. Soc. 35 (1972), 96-100. MR 0304586 (46:3721)
  • [4] N. Levinson, Generalization of an inequality of Ky Fan, J. Math. Anal. Appl. 8 (1964), 133-134. MR 28 #171. MR 0156928 (28:171)
  • [5] T. Popoviciu, Sur une inégalité de N. Levinson, Mathematica 6 (1964), 301-306.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A86

Retrieve articles in all journals with MSC: 26A86

Additional Information

Keywords: Inequality among means, generalized means, arithmetic means, geometric means
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society