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 boun...

Ramon Edgar Moore and Alexander M. Gofen introduced a generalization of Joseph Liouville's concept elementary functions. even defined two variants these, viz. scalar generalized functions vector functions, formulated conjecture concerning them. We prove that, for some modified conjectures, the classes are different.