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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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  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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