József Sándor and Barkat Ali Bhayo
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 4, Pages 1–10
Full paper (PDF, 178 Kb)
Details
Authors and affiliations
József Sándor
Babeș-Bolyai University, Department of Mathematics
Str. Kogălniceanu nr. 1, 400084 Cluj-Napoca, Romania
Barkat Ali Bhayo
Department of Mathematical Information Technology, University of Jyväskylä
40014 Jyväskylä, Finland
Abstract
Here authors establish the inequalities for two means X and Y studied in [11], and give the series expansion of these means.
Keywords
- Means and their inequalities
- Trigonometric functions
- Hyperbolic functions
- Series representation
AMS Classification
- 26D05
- 26D15
- 26D99
References
- Abramowitz, M., I. Stegun (Eds.), Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards, Dover, New York, 1965.
- Alzer, H., Two inequalities for means, C. R. Math. Rep. Acad. Sci. Canada, Vol. 9, 1987, 11–16.
- Alzer, H., S.-L Qiu, Inequalities for means in two variables, Arch. Math., Vol. 80, 2003, 201–205.
- Carlson, B. C., The logarithmic mean, Amer. Math. Monthly, Vol. 79, 1972, 615–618.
- Mitrinović, D. S., Analytic Inequalities, Springer–Verlag, Berlin, 1970.
- Neuman, E., J. Sándor, On the Schwab–Borchardt mean, Math. Pannonica, Vol. 14, 2003, No. 2, 253–266.
- Neuman, E., J. Sándor, On the Schwab–Borchardt mean II, Math. Pannonica, Vol. 17, 2006, No. 1, 49–59.
- Neuman, E., J. Sándor, Companion inequalities for certain bivariate means, Appl. Anal. Discr. Math., Vol. 3, 2009, 46–51.
- Neuman, E., J. Sándor, On certain means of two arguments and their extensions, Intern. J. Math. Sci., Vol. 16, 2003, 981–993.
- Sándor, J., Trigonometric and hyperbolic inequalities, 2011, http://arxiv.org/abs/1105.0859.
- Sándor, J., On two new means of two variables, Notes Number Th. Discr. Math., Vol. 20, 2014, No. 1, 1–9.
- Sándor, J., On the identric and logarithmic means, Aequat. Math., Vol. 40, 1990, 261–270.
- Sándor, J., A note on certain inequalities for means, Arch. Math. (Basel), Vol. 56, 1991, 471–473.
- Sándor, J., On certain identities for means, Studia Univ. Babes-Bolyai, Math., Vol. 38, 1993, 7–14.
- Sándor, J., On certain inequalities for means III, Arch. Math. (Basel), Vol. 67, 2001, 34–40.
- Sándor, J., New refinements of two inequalities for means, J. Math. Inequal., Vol. 7, 2013, No. 2, 251–254.
- Seiffert, H. J., Comment to Problem 1365, Math. Mag., Vol. 65, 1992, 356.
- Seiffert, H. J., Ungleichungen fur einen bestimmten Mittelwert, Nieuw Arch. Wiskunde (Ser. 4), Vol. 13, 1995, 195–198.
- Seiffert, H. J., Problem 887, Nieuw. Arch. Wisk., Vol. 11, 1993, 176.
Related papers
- Sándor, J. On two new means of two variables. Notes on Number Theory and Discrete Mathematics, Volume 20, 2014, Number 1, 1-9.
Cite this paper
Sándor, J. & Bhayo, B. A. (2014). On two new means of two variables II. Notes on Number Theory and Discrete Mathematics, 20(4), 1-10.