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Mean Value Theorems for Vector Valued Functions

Published online by Cambridge University Press:  20 January 2009

Robert M. McLeod
Robert M. McLeod
Affiliation:
American University of Beirut, Beirut, Lebanon
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The object of this paper is to give a generalisation to vector valued functions of the classical mean value theorem of differential calculus. In that theorem we have

for some c in the open interval a, b when f is a real valued function which is continuous on the closed interval a, b and differentiable on the open interval. The counterpart to (1) when f has values in an n-dimensional vector space turns out to be

where cka, b, 0 k, and .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 3 , June 1965 , pp. 197 - 209
Copyright
Copyright Edinburgh Mathematical Society 1965

References

REFERENCES

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