A note on bounds for the Neuman–Sándor mean using power and identric means

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 4, Pages 18–21
Full paper (PDF, 133 Kb)

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Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
Cluj-Napoca, Romania

Abstract

In this note we point out priority results and new proofs related to the bounds for the Neuman–Sándor mean in terms of the power means and the identric means.

Keywords

• Bounds
• Neuman–Sándor mean
• Identric mean
• Power mean

AMS Classification

• 26E60

References

1. Alzer, H. (1988), Aufgabe 987, Elemente der Mathematik, 43, 93.
2. Bullen, P. S. (2003), Handbook of means and their inequalities, Kluwer Acad. Publ.
3. Chu, Y.-M. & Long, B.-Y. (2013), Bounds of the Neuman–Sándor mean using power and identric means, Abstr. Appl. Anal., 2013, ID 832591, 6 pages.
4. Neuman, E. & Sándor, J. (2003) On the Schwab–Bachardt mean, Mathematica Pannonica, 14(2), 253–266.
5. Neuman, E. & Sándor, J. (2006) On the Schwab–Bachardt mean II, Mathematica Pannonica, 17(1), 49–59.
6. Neuman, E. & Sándor, J. (2009) Companion inequalities for certain bivariate means, Applicable Analysis Discr. Math., 3, 46–51.
7. Sándor, J. (1990) On the identric and logarithmic means, Aequationes Mathematicae, 40(1), 261–270.
8. Sándor, J. (1995) On certain inequalities for means, J. Math. Anal. Appl., 189, 602–606.
9. Sándor, J. (2001) On certain inequalities for means, III, Archiv der Mathematik, 76(1), 34– 40.
10. Yang, Z.-H. (2012) Sharp power mean bounds for Neuman–Sándor mean, http:// arxiv.org/abs/1208.0895.
11. Yang, Z.-H. (2013) Estimates for Neuman–Sándor mean by power means and their relative errors, J. Math. Ineq., 7(4), 711–726.