Some conditions for -convex functions

Author:
G. E. Cross

Journal:
Proc. Amer. Math. Soc. **82** (1981), 587-592

MSC:
Primary 26A51

MathSciNet review:
614883

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Abstract: It is shown that if is a function defined and continuous on such that (where is an even integer):

(a)

(b) for , where is countable, is -smooth, i.e.,

(c) a.e. in ;

(d) for where is countable and is -smooth in ; then is -convex in . The same result holds for odd. This is an improvement on the known result when is a scattered set.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0614883-1

Keywords:
Convex function

Article copyright:
© Copyright 1981
American Mathematical Society