By using the idea of substitution and constructing appropriate auxiliary functions,the Rolle's mean value theorem,Lagrange's mean value theorem,and Cauchy's mean value theorem were comprehensively extended.The application of these extended mean value theorems in proving differential equations and inequalities was explained through examples.
关键词
罗尔中值定理/拉格朗日中值定理/柯西中值定理/辅助函数/微分不等式
Key words
Rolle's mean value theorem/Lagrange's mean value theorem/Cauchy's mean value theorem/auxiliary function/differential inequality
维普
万方数据