Wavelet and Linear Algebra

Abstract As a generalization of convexity,  $ E $-convexity has been defined and studied in many publications. In this study, we recall the class of $ E $-$\mathbb {Q} $-convex sets, $ E $-$ \mathbb {Q}  $-convex and $ E $-additive functions and proved some properties of $ E $-$ \mathbb {Q}  $-convex functions.  Also, we develop the classical theorems of Jensen and Bernstein-Doetsch on $ E $-$ \mathbb {Q}  $-convex functions when vector spaces are over the rational numbers $ \mathbb {Q} $.