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

DOI:
https://doi.org/10.1090/S0002-9939-1977-0448394-2

MathSciNet review:
0448394

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-1977-0448394-2

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