A counterexample to the infinity version of the Hyers and Ulam stability theorem

Authors:
Emanuele Casini and Pier Luigi Papini

Journal:
Proc. Amer. Math. Soc. **118** (1993), 885-890

MSC:
Primary 26E15; Secondary 26B25, 46G99

MathSciNet review:
1152975

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Abstract: Hyers and Ulam proved a stability result for convex functions, defined in a subset of . Here we give an example showing that their result cannot be extended to those functions defined in infinite-dimensional normed spaces. Also, we give a positive result for a particular class of approximately convex functions, defined in a Banach space, whose norm satisfies the so-called convex approximation property.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1152975-X

Keywords:
Approximately convex functions,
Hyers and Ulam theorem,
convex approximation property

Article copyright:
© Copyright 1993
American Mathematical Society