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An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

DOI: 10.4236/jamp.2013.17001    2,419 Downloads   4,263 Views   Citations

ABSTRACT

In the present paper, we answer the question: for 0< a <1 fixed, what are the greatest value p(a)

and the least value q(a) such that the double inequality Jp(a,b)< aA(a,b)+ (1-a)G(a,b)<Jq(a,b)

holds for all a,b>0 with a is not equal to b ?

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Gao, H. , Li, S. , Zhang, Y. and Tian, H. (2013) An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means. Journal of Applied Mathematics and Physics, 1, 1-4. doi: 10.4236/jamp.2013.17001.

References

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