奇函数是特殊的中心对称函数,偶函数是特殊的轴对称函数.笔者在研究单调奇函数的性质时发现,当偶函数在y轴的一侧单调时,也会呈现出与单调奇函数类似的优美性质,而且这一性质还可推广到更一般的对称函数情形.本文称在原点(y轴)的一侧单调的奇(偶)函数为“单侧单调型”奇(偶)函数.下面就对此类函数进行探究:给出性质、推广,然后简述其应用.为了便于证明,首先给出如下结论: Odd function is a special central symmetry function and even function is a special axisymmetric function. When I study the properties of monotonic odd functions, I find that when the even function is monotonous on one side of the y axis, it will appear similar to monotonic odd functions , And this property can be generalized to the more general case of symmetric function. The monotonous odd (even) function on the side of the origin (y axis) is called “unilateral monotone” odd (even) Function. The following on this kind of function to explore: given the nature, promotion, and then briefly describe its application.In order to facilitate the proof, first of all, the following conclusions are given: