Advertisement

An Inequality Concerning Symmetric Functions and Some Applications

  • Dorin Andrica
  • Liviu Mare
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

An inequality for symmetric continuous functions E: I n → ℝ is proved in Theorem 1.1 and a variant for C 1 -differentiable functions is given in Theorem 1.2. Some applications concerning inequalities between means or convex functions are presented in the second section.

Key words and phrases

Symmetric functions Arithmetic, geometric and harmonic means Jensen’s inequality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Andrica and I. Raşa The Jensen inequality: refinements and applications, Anal. Numér. Théor. Approx. 14 (1985), 105–108.MathSciNetzbMATHGoogle Scholar
  2. 2.
    D. Andrica and M. O. Drimbe On some inequalities involving isotonic functionals, Anal. Numér. Théor. Approx. 17 (1988), 1–7.MathSciNetzbMATHGoogle Scholar
  3. 3.
    D. Andrica and L. Mare, An inequality concerning weighted-symmetric functions and applications, in preparation.Google Scholar
  4. 4.
    D. S. Mitrinović, Analytic Inequalities, Springer Verlag, Berlin — Heidelberg — New York, 1970.zbMATHGoogle Scholar
  5. 5.
    D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dodrecht — Boston — London, 1993.zbMATHGoogle Scholar
  6. 6.
    W. Sierpinski Sur un inégalité pour la moyenne arithmétiqe, géométrique et harmonique, Warsh. Sitzungsber. 2 (1909), 354–357.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Dorin Andrica
    • 1
  • Liviu Mare
    • 1
  1. 1.“Babes-Bolyai” UniversityCluj-NapocaRomania

Personalised recommendations