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EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

Published online by Cambridge University Press:  04 May 2015

IOSIF PINELIS*
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931, USA email [email protected]
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Abstract

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Exact upper and lower bounds on the difference between the arithmetic and geometric means are obtained. The inequalities providing these bounds may be viewed, respectively, as a reverse Jensen inequality and an improvement of the direct Jensen inequality, in the case when the convex function is the exponential.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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