On approximately convex functions
Author:
Zsolt Páles
Journal:
Proc. Amer. Math. Soc. 131 (2003), 243252
MSC (2000):
Primary 26A51, 26B25
Published electronically:
June 5, 2002
MathSciNet review:
1929044
Fulltext PDF Free Access
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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 Lipschitzmodulus. In the special case , the results reduce to that of Hyers, Ulam, and Green obtained in 1952 concerning the socalled convexity.
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Additional Information
Zsolt Páles
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H4010 Debrecen, Pf. 12, Hungary
Email:
pales@math.klte.hu
DOI:
http://dx.doi.org/10.1090/S0002993902065528
PII:
S 00029939(02)065528
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 T038072 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
