Some inequalities for arithmetic and geometric means
1999 ◽
Vol 129
(2)
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pp. 221-228
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Keyword(s):
Let An and Gn (respectively, A′n and G′n) be the weighted arithmetic and geometric means of x1, …, xn (respectively, 1 – x1, …, 1 – xn). We present sharp upper and lower bounds for the differences and . And we determine the best possible constants r and s such thatholds for all xi ∈ [a, b] (i = 1, …, n; 0 < a < b < 1). Our theorems extend and sharpen results of Fan, Cartwright and Field, McGregor and the author.
1999 ◽
Vol 42
(2)
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pp. 349-374
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Keyword(s):
1981 ◽
Vol 24
(3)
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pp. 257-271
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Keyword(s):
1996 ◽
Vol 120
(4)
◽
pp. 709-734
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2015 ◽
Vol 92
(1)
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pp. 149-158
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Keyword(s):
2013 ◽
Vol 94
(1)
◽
pp. 50-105
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Keyword(s):
2009 ◽
Vol 139
(4)
◽
pp. 709-718
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1983 ◽
Vol 95
(3-4)
◽
pp. 263-274
2009 ◽
Vol 147
(3)
◽
pp. 513-540
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Keyword(s):