Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T01:53:11.418Z Has data issue: false hasContentIssue false

Generalized mean value theorems of the differential calculus

Published online by Cambridge University Press:  09 April 2009

J. B. Diaz
Affiliation:
Rensselaer Polytechnic Institute Troy, New York 12181, U.S.A.
R. Výborný
Affiliation:
University of Queensland St. Lucia, 4067, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two generalized mean value theorems, for functions with values in a linear locally convex topological space, are proved, as consequences of two theorems for real valued functions of real variable.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Aziz, A. K. and Diaz, J. B. (1963), ‘On a mean value theorem of the differential calculus of vector valued functions’, Contributions to Differential Equations 1, 251269.Google Scholar
Averbuch, V. I. and Smoljanov, O. G. (1967), ‘Differential calculus in linear topological spaces’, (Russian), Usp. Mat. Nauk, 22 specially pages 201–2.Google Scholar
Diaz, J. B. and Výborný, R. (1964), ‘On mean value theorems for strongly continuous vector valued functions’, Contributions to Differential Equations 3, 107118.Google Scholar
Dieudonne, J. (1960), Foundations of Modern Analysis (New York, 1960), specially pages 153156.Google Scholar
McLeod, R. M. (19641965), ‘Mean value theorems for vector valued functions’, Proc. Edinburgh Math. Soc. 14, 197209.Google Scholar
Mlak, W. (1957), ‘Note on the mean value theorem’, Ann. Pol. Math. 3, 2931.CrossRefGoogle Scholar
Moss, R. M. J. and Roberts, G. T. (1968), ‘A creeping lemma’, Amer. Math. Monthly 75, 649652.Google Scholar
Wazewski, T. (1953), ‘Une generalisation des théorèmes sur les accroissements finis’, Ann. de la Societé Polonaise de Mathématiques 24, 132147.Google Scholar