Aequationes mathematicae

, Volume 87, Issue 3, pp 325–335

On generalized Seiffert means



Generalizations of two Seiffert means, usually denoted by P and T, are defined and investigated. The means under discussion are symmetric and homogeneous of degree one in each variable. Computable lower and upper bounds for the new means are also established. Several inequalities involving means discussed in this paper are obtained. In particular, two Wilker’s type inequalities involving those means are derived.

Mathematics Subject Classification (2000)

Primary 26E60 Secondary 33E05 26D07 


Seiffert means Schwab–Borchardt mean completely symmetric elliptic integral Wilker’s type inequalities 


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  1. 1.
    Borwein J.M., Borwein P.B.: Pi and AGM: A Study in Analyric Number Theory and Computational Complexity. Wiley, New York (1987)Google Scholar
  2. 2.
    Carlson B.C.: Algorithms involving arithmetic and geometric means. Am. Math. Mon. 78, 496–505 (1971)CrossRefMATHGoogle Scholar
  3. 3.
    Carlson B.C.: Special Functions of Applied Mathematics. Academic Press, New York (1977)MATHGoogle Scholar
  4. 4.
    Chu, Y.-M., Wang, M.-K., Qiu, S.-L., Qiu, Y.-F.: Sharp generalized Seiffert mean bounds for Toader mean. Abstr. Appl. Anal. Article ID 605259 (2011)Google Scholar
  5. 5.
    Kazi H., Neuman E.: Inequalities and bounds for elliptic integrals. J. Approx. Theory 146, 212–226 (2007)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Neuman E.: Inequalities for the Schwab–Borchardt mean and their applications. J. Math. Inequal. 5, 601–609 (2011)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Neuman E.: A note on a certain bivariate mean. J. Math. Inequal. 4, 637–643 (2012)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Neuman E.: On one-parameter family of bivariate means. Aequat. Math. 83, 191–197 (2012)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Neuman E.: Inequalities for weighted sums of powers and their applications. Math. Inequal. Appl. 15, 995–1005 (2012)MATHMathSciNetGoogle Scholar
  10. 10.
    Neuman, E.: A one-parameter family of bivariate means. J. Math. Inequal. (in press)Google Scholar
  11. 11.
    Neuman E., Sándor J.: On the Schwab–Borchardt mean. Math. Pannon. 14, 253–266 (2003)MATHMathSciNetGoogle Scholar
  12. 12.
    Neuman E., Sándor J.: On the Schwab–Borchardt mean II. Math. Pannon. 17, 49–59 (2006)MATHMathSciNetGoogle Scholar
  13. 13.
    Seiffert H.-J.: Problem 887. Nieuw. Arch. Wisk. 11, 176 (1993)Google Scholar
  14. 14.
    Seiffert H.-J.: Aufgabe 16. Würzel 29, 87 (1995)Google Scholar
  15. 15.
    Toader G.: Seiffert type means. Nieuw. Arch. Wisk. 17(3), 379–382 (1999)MathSciNetGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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