几个涉及参数的分式不等式(Ⅰ)

Several Inequalities of Fractional Ecpressions Involving Parameters

使用基本的与已知的不等式,将田彦武的一类涉及参数的分式不等式推广为更为一般情形与别的情形.例如,设ai>0(i=1,2,…,n),n 2,an+1=a1,an+2=a2,∑in=1api/2=1,且p 2,μ>0,λ>0,则有,∑ni=1aipλapi/+21+μapi+2>(1-4λ)-4μ,(ⅰ),如果在上述假设下还有0<a1 a2…an,那么,i∑=n1λapi+/21+aμipapi/+21api+/224-λ-μ4,(ⅱ).

Using some fundamental and given inequalities, several inequalities of fractional expressions in- volving parameters, which are due to Tian Yanwu, are generalized as more general cases and others. For example, if,ai〉0（i=1,2,…,n）,n≥2,an＋1=a1,an＋2=a2,∑i=1^nai^p/2=1 and p≥2,μ〉0,λ〉0,then ∑↓i=1↑nai^p/（λa（i＋1）^（p/2）＋μai^p＋2）〉（1-λ/4）-μ/4,（i）,Under the above hypothesis, if 0〈a1≤a2≤…≤an we have ∑↓i=1↑nai^p/（λa（i＋1）^p/2＋μa（i＋1）^p/2a（i＋2）^p/2）≥（4-λ-μ）/4,（ii）.