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On some mean value theorems of the differential calculus

Published online by Cambridge University Press:  17 April 2009

J.B. Diaz  and
R. Výborný
J.B. Diaz
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York, USA; University of Queensland, St Lucia, Queensland
R. Výborný
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York, USA.
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Abstract

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A general mean value theorem, for real valued functions, is proved. This mean value theorem contains, as a special case, the result that for any, suitably restricted, function f defined on [a, b], there always exists a number c in (a, b) such that f(c) − f(a) = f′(c)(c−a). A partial converse of the general mean value theorem is given. A similar generalized mean value theorem, for vector valued functions, is also established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 227 - 238
Copyright
Copyright © Australian Mathematical Society 1971

References

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