Limit Properties of Differential Mean Values

In this paper, we establish some results that concern the behavior of two types of differential mean values as the interval length shrinks to zero. The first type involves divided difference and the second type is connected to a theorem due to Flett w Math. Gazette 42 1958., 38]39x. We show that if a function f t. is of the form p t.q tya.ag t., where p t. is a polynomial, then the behavior of the limit is essentially independent of the function g t.. The results established by Bao-lin w Amer. Math. Monthly 104 1997., 561]562xand JacobsonwAmer. Math. Monthly 89 1982., 300]301x are special cases of our results