大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2012年
5期
140-143
,共4页
Lagrange微分中值定理%严格凸函数%严格凹函数%逆问题
Lagrange微分中值定理%嚴格凸函數%嚴格凹函數%逆問題
Lagrange미분중치정리%엄격철함수%엄격요함수%역문제
Lagrang's differential mid-value theorem%strictly convex function%strictly concave function%inverse problem
近年来，若干文章对“Lagrange微分中值定理的逆问题”进行了讨论，但其表述均不完整，且证明也较繁琐。本文使用严格凸（严格凹）函数的性质，给出该问题一个条件较弱且表述较完整的结果，其证明也较简洁。
近年來，若榦文章對“Lagrange微分中值定理的逆問題”進行瞭討論，但其錶述均不完整，且證明也較繁瑣。本文使用嚴格凸（嚴格凹）函數的性質，給齣該問題一箇條件較弱且錶述較完整的結果，其證明也較簡潔。
근년래，약간문장대“Lagrange미분중치정리적역문제”진행료토론，단기표술균불완정，차증명야교번쇄。본문사용엄격철（엄격요）함수적성질，급출해문제일개조건교약차표술교완정적결과，기증명야교간길。
In recent years, the some papers discuss the“ inverse problem of Lagrang's differential mid-value theorem ”, but their expressions are not complete, and their proof are more verbose. In this paper, by the properties of strictly convex (strictly concave) function, we give a weak condition and more complete results for “ inverse problem of Lagrang' s differential mid-value theorem ”, and its proof is more concise.
