Some new types of the NCP-functions and their properties

Abstract

在這篇論文當中，我們觀察出一些互補函數是由可逆函數構造出來，像是有名的費雪-博美斯特函數。根據類似的結構，我們利用可逆函數 e^t 和 ln⁡t發現了其他兩個互補函數。我們還發現了另一種的互補函數，它們是在費雪-博美斯特函數的-a和-b這兩項的前面分別乘上滿足特定條件的連續函數。在第四節中，我們討論這三種互補函數的一般形式，並給一些例子和函數的圖形。一些相關的應用和數值的實驗可以當作是後續研究的主題。

In this thesis, we observed that some of the NCP functions were constructed by invertible functions. For example, the famous Fischer-Burmeister function was constructed under this presence. According to the similar structure of the Fischer-Burmeister function, we discovered the other two NCP functions accociated with the invertible functions which were e^t and ln⁡t. We also discovered another type of NCP function which was modified by multiplying the continuous function satisfying the required assumptions infront of the terms -a and -b of the Fischer-Burmeister function . In the section 4, we discussed the general format of the three newly discovered NCP functions and gave some examples and graphs of the different types of NCP functions. We leave some other possible applications and numerical tests of those NCP functions as our future reseach topics.