一个双参数二元不等式的推广

Extension of an Inequality of Two Variables With Two Parameters

二元不等式aars--bbrs≥rsa+2bs-r成立或反向成立的充分条件是被学者广泛关注的问题。通过变换a=bx将该不等式转化为一元不等式,并结合简单的分析手段较大地扩展了参数r,s的取值范围。

Abstract： The fact that the sufficient condition of the inequality of two variables a^s-b^s/a^r-b^r≥s/r（a＋b/2）^s-r and its reverse are valid has aroused the interest of a number of scholars. By the transformation a = bx, the above inequality is reduced to an inequality of a variable, and the range of the parameters r, s is extended largely with simple method of the analysis.