On relation between the power mean and the logarithmic mean
碩士 === 淡江大學 === 數學學系碩士班 === 94 === If x , y are distinct positive numbers, then Mp= Mp (x , y) is called the power mean of x and y . L = L (x , y) is called the Logarithmic mean of x and y . Chang[2]has proved that : If L < Mq holds for some q such that q<1/3 ，as well as Mp < L holds for...
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| Other Authors: | |
| Format: | Others |
| Language: | zh-TW |
| Published: |
2004
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| Online Access: | http://ndltd.ncl.edu.tw/handle/77822405531767593642 |
| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 94 === If x , y are distinct positive numbers, then
Mp= Mp (x , y)
is called the power mean of x and y .
L = L (x , y)
is called the Logarithmic mean of x and y .
Chang[2]has proved that :
If L < Mq holds for some q such that q<1/3 ，as well as Mp < L holds for some p such that p>0 under certain restrictions on x and y 。.
We shall prove that L < Mq holds for some q such that q <1/6 , as well as L > Mp holds for some p such that p > 0 under certain restrictions on x and y .
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