CAJ | 학술논문

运用极限的思想以及函数的泰勒展开证明不等式Jp(a,b)＜H(a,b)＜Jq(a,b)成立.找到使得双向不等式Jp(a,b)＜(H)(a,b)＜Jq(a,b)对于所有的a,b＞0以及a≠b都成立的最大值p和最小值q,这里Jp(a,b)和(H)(a,b)分别定义为两个正整数a和b的阶为p的一参数均值和Heron均值.
운용겁한적사상이급함수적태륵전개증명불등식Jp(a,b)＜H(a,b)＜Jq(a,b)성립.조도사득쌍향불등식Jp(a,b)＜(H)(a,b)＜Jq(a,b)대우소유적a,b＞0이급a≠b도성립적최대치p화최소치q,저리Jp(a,b)화(H)(a,b)분별정의위량개정정수a화b적계위p적일삼수균치화Heron균치.
Using the thinking method of limit and taylor expansion of the function,the paper presented that Jp(a,b)＜(H)(a,b)＜Jq(a,b) holds for a,b＞0 with a≠b,and found the greatest value p and the least value q such that the double inequality Jp(a,b)＜(H)(a,b)＜Jq(a,b) holds for all a,b＞0 with a≠b,where Jp(a,b) and (H)(a,b) denote the one-parameter of order p and Heron means of two positive real number a and b,respectively.