P-adic数域上的微分中值定理

Mean Value Theorem of Differentials on P-adic Fields

主要研究P-adic数域上的微分中值定理。在给出导数定义的前提下,对P-adic变量实值函数和P-adic值函数微分中值定理作了完整的证明。并分析了实数域与P-adic数域上微分中值定理的异同。

The paper is briefly focused on mean value theorem of differentials on P-adic fields. On the premise of definition, we proved the mean value theorem of differentials of P-adic variable function particularly. And compared the difference between real analysis and P-adic analysis on mean value theorem of differentials.