Generalized approximate midconvexity

@inproceedings{Tabor2009GeneralizedAM,
  title={Generalized approximate midconvexity},
  author={Jacek Tabor and Jơzef Tabor},
  year={2009}
}
The existing various notions of generalized convexity are very useful, in particular in optimal control theory (Cannarsa and Sinestrari, 2004) and optimization (for more information and references see Rolewicz, 2005). Therefore, convenient conditions which guarantee generalized convexity are very useful. As we know from the classical theory of convex functions, midconvexity and local upper boundedness guarantee convexity. Not surprisingly, a similar type of behaviour 

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