Banach空间中连续真函数的误差界成立的广义三阶条件
Generalized Third-Order Conditions for Error Bound of Proper Functions in Banach Spaces

利用了函数二阶方向导数，在Bananch空间连续函数误差界成立的一、二阶充分条件的基础上首次得到了广义三阶充分条件。此条件的给出不仅提供了检验函数误差界成立的依据，更由于研究方法的独特性，在一、二阶充分条件失效的情形下给出了验证误差界的方法和手段。
： By using the second-order directional derivatives, ~an extend third-order sufficient condition ensuring that a proper continuous function on a Banach space has an error bound is established in this paper for the first time, which is based above the first and second order sufficient conditions. This result makes it be possible to ensure the existence of the error bound in the cases that the first or second order sufficient conditions don't work