Injectiveness and Discontinuity of Multiplicative Convex Functions

Abstract

In the present work we study the set of multiplicative convex functions. In particular, we focus on the properties of injectiveness and discontinuity. We will show that a non constant multiplicative convex function is at most 2-injective, and construct multiplicative convex functions which are discontinuous at infinitely many points.

Keywords

• convexity
• convex function
• multiplicative convex