A Summary of Convexity and Generalized Convexities

In this paper we would give a summary to the convexities of sets and functions to provoke people's researching interest to generalized convexity.The ordinary convexity,geometrical convexity,logarithmical convexity and the exponential convexity are mentioned in the first two sections;the ideal convexity,integral convexity and the β-convextiy are presented in the central three sections;for the more generalized convexties are briefly introduced in the last section.