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

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran.

2 Department of Mathematics‎, ‎Faculty of Science, Shahid Rajaee Teacher Training University, P.O‎. ‎Box 16785-136‎, ‎Tehran‎, ‎Iran.

10.22072/wala.2023.2003060.1422

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} $.

Keywords

References

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Wavelet and Linear Algebra
Volume 10, Issue 2
Autumn- Winter
2023
Pages 63-69

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