Refinement of some inequalities for means

Authors

  • Mira-Cristiana Anisiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
  • Valeriu Anisiu "Babeş-Bolyai" University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat351-1005

Keywords:

inequalities, asymptotic developments, symbolic algebra
Abstract views: 224

Abstract

We consider weighted arithmetic means as, for example, \(\alpha G+(1-\alpha)C,\) with \(\alpha\in(0,1)\), \(G\) \(C\) being the geometric and anti-harmonic means, and we find the range of values of \(\alpha\) for which the weighted mean is still greater or less than some suitable means, in this case the arithmetic and Hölder ones.

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References

Bullen, P. S., Handbook of Means and Their Inequalities, Series: Mathematics and Its Applications, vol. 560, 2nd ed., Kluwer Academic Publishers Group, Dordrecht, 2003.

Ivan, M. and Raşa, I., Some inequalities for means, Tiberiu Popoviciu Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca, May 23-29, pp. 99-102, 2000.

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Published

2006-02-01

How to Cite

Anisiu, M.-C., & Anisiu, V. (2006). Refinement of some inequalities for means. Rev. Anal. Numér. Théor. Approx., 35(1), 5–10. https://doi.org/10.33993/jnaat351-1005

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