高阶Cauchy中值定理中间点函数渐近性与可微性的再研究

Again study the asymptotic behavior and the differentiability of intermediate point function for high order Cauchy mean value theorem

利用比较函数概念,研究高阶Cauchy中值定理中间点函数的渐近性,在一定条件下,建立了高阶Cauchy中值定理中间点函数更广泛的渐近估计式;作为推论还获得了高阶Cauchy中值定理中间点函数的一阶可微性.所得结果推广和改进了有关文献中的结果,丰富了中值定理理论.

By using the concept of comparison function, the asymptotic behavior of the intermediate point function of the high order Cauchy mean value theorem was studied. Under certain conditions, a broader asymptotic estimate of the intermediate point function of the high order Cauchy mean value theorem was established. The first-order differentiability of the intermediate point function of the high order Cauchy mean value theorem was obtained. The obtained results generalized and improved the results in the relevant literature,and enriched the theory of the median theorem.