Inequalities Between Reciprocals of Means
DOI:
https://doi.org/10.5644/SJM.11.2.04Keywords:
Means, asymptotic expansion, inequalitiesAbstract
The subject of this paper is linear combinations of reciprocal values of classical bivariate means and their behavior for translated values of the arguments. Based on the known asymptotic expansions some optimal parameters were obtained.
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References
J. Aczel and Z. P´ales, The behaviour of means under equal increments, Am. Math. Mon., 95 (1988), 856–860.
P. S. Bullen, Averages still on the move, Math. Mag., 63 (1990), 250–255.
P. S. Bullen, A Dictionary of Inequalities, Chapman & Hall, 1998.
P. S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publishers, 2003.
P. S. Bullen, D. S. Mitrinovi´c and P. M. Vasi´c, Means and Theirs Inequalities, D Reidel, Dordrecht, 1988.
T. Buri´c, N. Elezovi´c and R. Simi´c, ˇ Asymptotic expansions of the multiple quotients of gamma functions and applications, Math. Inequal. Appl. 16 (4) (2013), 1159–1170.
C.-P. Chen, On Some Inequalities for Means and the Second Gautschi-Kershaw’s Inequality, RGMIA 11 (2008), Supplement, art. 6.
C.-P. Chen, N. Elezovi´c and L. Vukˇsi´c, Asymptotic formulae associated with the Wallis power function and digamma function, J. Class. Anal., 2 (2) (2013), 151–166.
N. Elezovi´c, Asymptotic inequalities and comparison of classical means, J. Math. Inequal., 9 (1) (2015), 177–196.
N. Elezovi´c and L. Vukˇsi´c, Asymptotic expansions of bivariate classical means and related inequalities, J. Math. Inequal., 8 (4) (2014), 707–724
N. Elezovi´c and L. Vukˇsi´c, Asymptotic expansions and comparison of bivariate parameter means, Math. Inequal. Appl., 17 (4) (2014), 1225–1244.
L. Hoehn and I. Niven, Averages on the move, Math. Mag., 58 (1985), 151–156.
W.-D. Jiang, Some sharp inequalities involving reciprocals of the Seiffert and other means, J. Math. Inequal., 4 (6) (2012), 593–599.
D. S. Mitrinovi´c, J. E. Peˇcari´c and A. M. Fink, Classical and New Inequalities in Analysis, D Reidel, Dordrecht, 1993.
E. Neuman and J. S´andor, On certain new means of two arguments and their extensions, Int. J. Math. Math. Sci., 16 (2003), 981–993.
J. S´andor, On the identric and logarithmic means, Aequationes Math. 40 (1990), 261–270.
J. S´andor, On certain inequalities for means II, J. Math. Anal. Appl., 199 (1996), 629–635.
J. S´andor, On certain inequalities for means III, Arch. Math., 76 (2001), 34–40.
J. S´andor, On Huygens’ inequalities and the theory of means, Int. J. Math. Math. Sci., (2012), article ID 597490, 9 pages.
H.-J. Seiffert, Ungleichungen f¨ur einen bestimmten Mittelwert, Nieuw Arch. Wiskd., (4) 13 (2) (1995), 195–198.
A. Witkowski, Interpolations of Schwab-Borchardt mean, Math. Inequal. Appl., 16 (1) (2013), 193–206.
