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On one-parameter family of bivariate means

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Abstract

A one-parameter family of bivariate means is introduced. They are defined in terms of the inverse functions of Jacobian elliptic functions cn and nc. It is shown that the new means are symmetric and homogeneous of degree one in their variables. Members of this family of means interpolate an inequality which connects two Schwab–Borchardt means. Computable lower and upper bounds for the new mean are also established.

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References

  1. Borwein J.M., Borwein P.B.: Pi and AGM: A Study in Analytic Number Theory and Computational Complexity. Wiley, New York (1987)

    MATH  Google Scholar 

  2. Carlson B.C.: Algorithms involving arithmetic and geometric means. Am. Math. Mon. 78, 496–505 (1971)

    Article  MATH  Google Scholar 

  3. Carlson B.C.: Special Functions of Applied Mathematics. Academic Press, New York (1977)

    MATH  Google Scholar 

  4. Neuman, E.: Inequalities for the Schwab-Borchardt mean and their applications. J. Math. Inequal. (2011, in press)

  5. Neuman, E.: Product formulas and bounds for Jacobian elliptic functions with applications. Integral Transforms Spec. Funct. (2011, in press)

  6. Neuman E., Sándor J.: On the Schwab-Borchardt mean. Math. Pannon. 14(2), 253–266 (2003)

    MathSciNet  MATH  Google Scholar 

  7. Neuman E., Sándor J.: On the Schwab-Borchardt mean II. Math. Pannon. 17(1), 49–59 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W. (eds): The NIST Handbook of Mathematical Functions. Cambridge University Press, New York (2010)

    Google Scholar 

  9. Seiffert H.-J.: Problem 887. Nieuw. Arch. Wisk. 11, 176 (1993)

    Google Scholar 

  10. Seiffert H.-J.: Aufgabe 16. Würzel 29, 87 (1995)

    Google Scholar 

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  1. Department of Mathematics, Southern Illinois University, Mailcode 4408, 1245 Lincoln Drive, Carbondale, IL, 62901, USA

    Edward Neuman

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  1. Edward Neuman
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Correspondence to Edward Neuman.

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Neuman, E. On one-parameter family of bivariate means. Aequat. Math. 83, 191–197 (2012). https://doi.org/10.1007/s00010-011-0099-5

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  • DOI: https://doi.org/10.1007/s00010-011-0099-5

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