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On approximately Breckner s-convex functions

Burai P., Hazy A., Juhasz T.

Control and Cybernetics

2011

Vol. 40, no 1

91-99

The main goal of this paper is to consider the regularity and convexity properties of a given type of approximately generalized convex functions, namely approximately Breckner s-convex functions (see the origin of the definition in Breckner, 1978). Our main result is a Bernstein-Doetsch type one. It is proved that the local boundedness of such a type of function from above at a point of its domain implies approximate convexity and stronger regularity properties of the function in question on the whole domain.