設f為開區間I上的連續函數,a∈I。

我們定義L_a與P_a如下:

L_a (t)≔(f(t)+f(a))/2 (t-a)-∫_a^t〖f(s)ds,a≤t〗 。

P_a (t)≔∫_a^tf(s)ds-(t-a)f((t+a)/2),a≤t。

我們考慮L_a與P_a的凸性的相關問題及其反問題。

Let f be continuous function in open interval I and a∈I.

We define

L_a (t)≔(f(t)+f(a))/2 (t-a)-∫_a^t〖f(s)ds,a≤t〗 。

P_a (t)≔∫_a^tf(s)ds-(t-a)f((t+a)/2),a≤t。

We study the properties of L_a and P_a.

1.第一章 前言……………………………………1

2.第二章 主要結果………………………………15

3.參考文獻 ………………………………………35

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