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Continuity of real valued subquadratic functions. (English) Zbl 1292.26031
Summary: The aim of this paper is to prove a regularity theorem for real valued subquadratic mappings that are solutions of the inequality
$\varphi(x+y)+\varphi(x-y)\leq 2\varphi(x)+2\varphi(y),\quad x,y\in X\,,$
where $$X=(X,+)$$ is a topological group.

##### MSC:
 26A51 Convexity of real functions in one variable, generalizations