湖州师范学院学报
湖州師範學院學報
호주사범학원학보
JOURNAL OF HUZHOU TEACHERS COLLEGE
2011年
1期
1-6
,共6页
单参数平均%对数平均%指数平均
單參數平均%對數平均%指數平均
단삼수평균%대수평균%지수평균
one-parameter mean%logarithmic mean%identric mean
利用初等微分学比较了单参数平均与对数和指数平均的几何组合,发现了使得双向不等式Jp(a,b)＜Ia(a,b)L1-a(a,b)＜J,q(a,b)对a∈(o,√17-3/2]和所有a,b＞0且a≠b成立的p的最大值和q的最小值,其中Jp(a,b),L(a,b)和I(a,b)分别表示a与b的p-次单参数平均、对数平均和指数平均.
利用初等微分學比較瞭單參數平均與對數和指數平均的幾何組閤,髮現瞭使得雙嚮不等式Jp(a,b)＜Ia(a,b)L1-a(a,b)＜J,q(a,b)對a∈(o,√17-3/2]和所有a,b＞0且a≠b成立的p的最大值和q的最小值,其中Jp(a,b),L(a,b)和I(a,b)分彆錶示a與b的p-次單參數平均、對數平均和指數平均.
이용초등미분학비교료단삼수평균여대수화지수평균적궤하조합,발현료사득쌍향불등식Jp(a,b)＜Ia(a,b)L1-a(a,b)＜J,q(a,b)대a∈(o,√17-3/2]화소유a,b＞0차a≠b성립적p적최대치화q적최소치,기중Jp(a,b),L(a,b)화I(a,b)분별표시a여b적p-차단삼수평균、대수평균화지수평균.
We compare the one-parameter mean with the geometric combination of logarithmic and identric means by use of the elementary differential calculus,and find the greatest value p=p(a) and the smallest value q = q(a)such that the double inequality Jp(a,b)＜ P(a,b)L1-a(a,b)＜Jq(a,b) holds for a∈ (0,√17-3/2] and all a,b＞0 with a≠b＜ where J p(a,b) ,L(a,b) and I(a,b) denote the p-th one-parameter,logarithmic,and identric means of a and b,respectively.
