The Multidirectional Mean Value Theorem in Banach Spaces

Abstract

AbstractRecently, F. H. Clarke and Y. Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certain Banach spaces, namely those that admit a C1-Lipschitz continuous bump function.