# Accession Number:

## AD0261013

# Title:

## ON A MEAN VALUE THEOREM OF THE DIFFERENTIAL CALCULUS OF VECTOR VALUED FUNCTIONS, AND UNIQUENESS THEOREMS FOR ORDINARY DIFFERENTIAL EQUATIONS IN A LINEAR NORMED SPACE

# Descriptive Note:

# Corporate Author:

## NAVAL ORDNANCE LAB WHITE OAK MD

# Report Date:

## 1961-05-16

# Pagination or Media Count:

## 23.0

# Abstract:

Suppose that 1 the vector valued function xt is defined for all real t such that a t b, where a b, and that its values are in a linear normed vector space B the norm in B will be denoted by 2 limt ax T x a and limt bxt xb i.e., for example limt a xt - xa 0 3 the derivative xt exists, and is finite, whenever a t b i.e., there is a vector xt in the space B such that lims t xs - xts-t xt 0. Then there is a number , with a b, such that xb-xab-a x . This mean value theorem for vector valued functions is proved first, and then it is used to derive uniqueness theorems for the vector initial value problem dxdt ft,x sto xo. Author