關于冪函數(shù)的一致連續(xù)性問題

白占強

摘 要 一致連續(xù)性是連續(xù)函數(shù)的一個非常重要的性質(zhì)， 它刻劃出了函數(shù)在一個區(qū)間上的全局性。冪函數(shù)是一類非常重要的基本初等函數(shù)。對于冪函數(shù)的一致連續(xù)性，我們從幾個常見例子出發(fā)來探討下它們的一致連續(xù)性問題。本文主要討論冪函數(shù)在區(qū)間（0，+）上的一致連續(xù)性。

關鍵詞 一致連續(xù) 冪函數(shù) 一致連續(xù)性判定

中圖分類號：O174 文獻標識碼：A DOI：10.16400/j.cnki.kjdkx.2018.06.027

Abstract Uniform continuity is a very important property of a continuous function， which sculpts the global nature of the function over an interval. The power function is a very important elementary function. For the consistent continuity of power functions， we start from a few common examples to discuss their uniform continuity problems. This article focuses on the consistent continuity of the power function over the interval.

Keywords uniform continuity； power function； uniform continuity determination