Abstract
In this paper, the authors find the best numbers α and β such that
for all a,b>0 with a≠b, where \( \bar{C}(a,b)=\frac{2(a^{2}+ab+b^{2})}{3(a+b)}\) and \(T(a,b)=\frac {2}{\pi }{\int }_{0}^{{\pi }/{2}}\sqrt {a^{2}{\cos ^{2}{\theta }}+b^{2}{\sin ^{2}{\theta }}}\, \mathrm {d} \theta \) denote respectively the centroidal mean and Toader mean of two positive numbers a and b.
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Acknowledgements
The authors would like to thank the anonymous referee for his/her careful reading and helpful corrections to the original version of this paper. The first author was partially supported by the Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J11LA57, China.
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HUA, Y., QI, F. A double inequality for bounding Toader mean by the centroidal mean. Proc Math Sci 124, 527–531 (2014). https://doi.org/10.1007/s12044-014-0183-6
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DOI: https://doi.org/10.1007/s12044-014-0183-6