A study on the continuity of some classes of E -\mathbb {Q} -convex functions

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} .

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قضیه برنشتاین-دتچ ، مجموعه ای-محدب ، تابع تقریبا ای-محدب ، تابع ای-گویا-محدب و مجموعه ای-گویا-محدب