(a,b)-Convex Functions

• Main Authors: Wen-Hua Lin, 林文化
• Other Authors: Jin-Chirng Lee
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/15757279667918426000

碩士 === 中原大學 === 應用數學研究所 === 96 === Abstract The theory of (a,b)-convex functions was introduced by Norber Kuhn in 1987【1】.Kuhn focused mainly on the structure and the properties of (a,b)-convex functions.And we generalize a result raised by Zygfryd Kominek in 1992【2】.He would like to know on what conditions under which an (a,b)-convex function is a constant function. Given a function f：I→[－∞ , ∞），we define the following three sets： (Ⅰ) K’(f)＝﹛(a,b)€(0,1)×(0,1) | f is an (a,b)-convex function﹜ (Ⅱ) K(f)＝﹛a€(0,1) | f is an a-convex function﹜ (Ⅲ) A’(f)＝﹛(a,b)€(0,1)×(0,1) | f is an (a,b)-affine function﹜ We proceed to discuss the properties of these sets K’(f)、K(f) and A’(f).Then we show that，if f：I→[－∞ , ∞）is a continuous (a,b)-convex function，f is a convex function. Finally we prove that，if (a,b)€K’(f)，a≠b and a€Q ，then f is a constant function.