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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A converse of Taylor's theorem for functions on Banach spaces


Author: S. Dayal
Journal: Proc. Amer. Math. Soc. 65 (1977), 265-273
MSC: Primary 58C20; Secondary 46G05
MathSciNet review: 0448394
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Abstract: The main results are the local representation theorems associating the local weak n-Taylor series expansion of a function defined on a Banach space to a local n-Taylor series expansion of the coefficients. These theorems are used to prove a converse of Taylor's theorem which uses weaker hyptohesis than used by others. Another useful application of the above results is done in [2] to study a class of functions called n-convex functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0448394-2
PII: S 0002-9939(1977)0448394-2
Keywords: Fréchet differential, strong differential, multilinear functions, discrete differences, convex property, convex set, local representations, weak and strong n-Taylor series expansion
Article copyright: © Copyright 1977 American Mathematical Society