We give an elementary framework of generalized convexity in terms of comparison of a given function with reference functions from a chosen set. As important examples we consider reference sets used in Alexandrov geometry and give simple proofs for the characterization of generalized convexity in form of differential inequalities.
The current online version of this article, posted on 5 October 2022, supersedes an earlier version posted on 13 June 2022. The volume and issue information have been corrected.
"Generalized Convexity and Passage from Local to Global via Differential Inequalities." Real Anal. Exchange 47 (1) 103 - 120, 2022. https://doi.org/10.14321/realanalexch.47.1.1602263520