Bilateral inequalities for means

Authors

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

DOI:

https://doi.org/10.33993/jnaat422-985

Keywords:

two-variable means, weighted arithmetic mean, inequalities, symbolic computer algebra
Abstract views: 211

Abstract

Let \(\left(M_{1},M_{2},M_{3}\right) \) be three means in two variables chosen from \(H\), \(G\), \(L\), \(I\), \(A\), \(Q\), \(S\), \(C\) so that \[ M_{1}(a,b)<M_{2}(a,b)<M_{3}(a,b),\quad 0<a<b. \] We consider the problem of finding \(\alpha,\ \beta\in\mathbb{R}\) for which \[ \alpha M_{1}(a,b)+(1-\alpha)M_{3}(a,b)<M_{2}(a,b)<\beta M_{1}(a,b)+(1-\beta )M_{3}(a,b). \] We solve the problem for the triplets \(\left(G,L,A\right)\), \(\left(G,A,Q\right)\), \(\left(G,A,C\right)\), \(\left(G,Q,C\right)\), \(\left(A,Q,C\right) \), \(\left(A,S,C\right) \), \(\left(A,Q,S\right) \) and \((L,A,C)\). The Symbolic Algebra Program Maple is used to determine the range where some parameters can vary, or to find the minimal polynomial for an algebraic number.

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References

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Published

2013-08-01

How to Cite

Anisiu, M.-C., & Anisiu, V. (2013). Bilateral inequalities for means. Rev. Anal. Numér. Théor. Approx., 42(2), 94–102. https://doi.org/10.33993/jnaat422-985

Issue

Vol. 42 No. 2 (2013)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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