On approximately convex functions

Author:
Zsolt Páles

Journal:
Proc. Amer. Math. Soc. **131** (2003), 243-252

MSC (2000):
Primary 26A51, 26B25

Published electronically:
June 5, 2002

MathSciNet review:
1929044

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Abstract | References | Similar Articles | Additional Information

Abstract: A real valued function defined on a real interval is called -convex if it satisfies

The main results of the paper offer various characterizations for -convexity. One of the main results states that is -convex for some positive and if and only if can be decomposed into the sum of a convex function, a function with bounded supremum norm, and a function with bounded Lipschitz-modulus. In the special case , the results reduce to that of Hyers, Ulam, and Green obtained in 1952 concerning the so-called -convexity.

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Additional Information

**Zsolt Páles**

Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary

Email:
pales@math.klte.hu

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06552-8

Keywords:
Convexity,
$(\varepsilon,\delta)$-convexity,
stability of convexity,
$(\varepsilon,\delta)$-subgradient,
$(\varepsilon,\delta)$-subdifferentiability

Received by editor(s):
April 2, 2001

Received by editor(s) in revised form:
September 4, 2001

Published electronically:
June 5, 2002

Additional Notes:
This research was supported by the Hungarian Scientific Research Fund (OTKA) Grant T-038072 and by the Higher Education, Research and Development Fund (FKFP) Grant 0215/2001.

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2002
American Mathematical Society