积分型中值定理中间点函数的性质

BEHAVIOR OF “INTERMEDIATE POINT FUNCTION” FOR INTEGRALS TYPE MEAN VALUE THEOREM

利用比较函数概念研究积分型中值定理"中间点函数"的渐近性,在函数f(x)和g(x)满足Ag(a)C_n^(ψ)≠Bf(a)C_n^(φ)等一些条件下,建立了积分型中值定理"中间点函数"更广泛的渐近性态,进而获得了"中间点函数"在点a处的一阶可微性,本文结果改进和推广了有关文献中的相应结果。

The asymptotic behavior of the intermediate point function of the integrals typemean value theorem is studied by using the concept of comparison function.The more extensive asymptotic behavior of the intermediate point function of the integrals mean value theorem are establishedunder the assumption thatthe functions f(x)and g(x)satisfy the conditions,such as Ag(a)Cn^(ψ)≠Bf(a)Cn^(ψ).Furthermore,the first order differentiability at a point of the intermediate point function was achieved for integrals typemean value theorem.The results in this paper improve and generalize the results in.