- Konuralp Journal of Mathematics
- Vol: 5 Issue: 1
- OPTIMAL WEIGHTED GEOMETRIC MEAN BOUNDS OF CENTROIDAL AND HARMONIC MEANS FOR CONVEX COMBINATIONS OF L...
OPTIMAL WEIGHTED GEOMETRIC MEAN BOUNDS OF CENTROIDAL AND HARMONIC MEANS FOR CONVEX COMBINATIONS OF LOGARITHMIC AND IDENTRIC MEANS
Authors : Ladislav Matejicka
Pages : 77-84
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Publication Date : 2017-04-01
Article Type : Research
Abstract :In this paper, optimal weighted geometric mean bounds of centroidal and harmonic means for convex combination of logarithmic and identric means are proved. We find the greatest value $\gamma(\alpha)$ and the least value $\beta(\alpha)$ for each $\alpha\in (0,1)$ such that the double inequality: $C^{\gamma(\alpha)}(a,b)H^{1-\gamma(\alpha)}(a,b)<\alpha L(a,b)+({1-\alpha})I(a,b)Keywords : Convex combinations bounds, centroidal mean, harmonic mean, weighted geometric mean, logarithmic mean, identric mean.