Rad HAZU, Matematičke znanosti, Vol. 19 (2015), 117-127.

ASYMPTOTIC BEHAVIOUR OF THE ITERATIVE ASYMPTOTIC BEHAVIOUR OF THE ITERATIVE

Tomislav Burić

Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
e-mail: tomislav.buric@fer.hr

Abstract.   Asymptotic expansion and behaviour of the iterative combinations of the Pythagorean means (arithmetic, geometric and harmonic mean) is obtained and analyzed. Results are used for asymptotic comparison of means.

2010 Mathematics Subject Classification.   26E60, 41A60.

Key words and phrases.   Pythagorean means, iterative means, arithmetic-geometric mean, asymptotic expansions.

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References:

  1. P. Bracken, An arithmetic-geometric mean inequality, Expo. Math. 19 (2001), 273-279.
    MathSciNet     CrossRef

  2. P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publisher, Dordrecht, 2003.
    MathSciNet     CrossRef

  3. P. S. Bullen, D. S. Mitrinović and P. M. Vasić, Means and theirs inequalities, D. Reidel Publishing Co., Dordrecht, 1988.
    MathSciNet     CrossRef

  4. T. Burić and N. Elezović, Asymptotic expansion of the arithmetic-geometric mean and related inequalities, J. Math. Inequal. 9 (2015), 1181-1190.
    MathSciNet     CrossRef

  5. N. Elezović, Asymptotic inequalities and comparison of classical means, J. Math. Inequal. 9 (2015), 177-196.
    MathSciNet     CrossRef

  6. N. Elezović and L. Vukšić, Asymptotic expansions of bivariate classical means and related inequalities, J. Math. Inequal. 8 (2014), 707-724.
    MathSciNet     CrossRef

  7. N. Elezović and L. Vukšić, Asymptotic expansions and comparison of bivariate parameter means, Math. Inequal. Appl. 17 (2014), 1225-1244.
    MathSciNet     CrossRef

  8. M. K. Vamanamurthy and M. Vuorinen, Inequalities for means, J. Math. Anal. Appl. 183 (1994), 155-166.
    MathSciNet     CrossRef

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