An Extension of the Dieudonne's Mean Value Theorem

Abstract

In this paper we extend the Dieudonne's mean value theorem to the f(x) which is a mapping of 〔a,b〕into a topological linear space and the Ø(x) which is a continuous realvalued function on 〔a,b〕. One of the sufficient conditions is the existence of the right derivative of f. Particulary, if f(x) is a mapping of 〔a,b〕into〔c,d〕, the sufficient condition can be relaxed to the existence of the Dini derivative.