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

IOSIF PINELIS
2015 Bulletin of the Australian Mathematical Society  

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2015 pre-print arXiv:1503.00345v1 fatcat:7uak7kmjjnfz3caqxwmnbytbou

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2015 accepted
arXiv:1503.00345v2 fatcat:7pbjug6cbrg3hfiqfbapq4gdbm
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.
doi:10.1017/s0004972715000350 fatcat:qrh4b7hs3ndhleodmcwaq2sf2y
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IOSIF PINELIS. "EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS." Bulletin of the Australian Mathematical Society 92.1 (2015) 1-10