Continuity of real valued subquadratic functions. (English) Zbl 1292.26031

Kominek, Zygfryd; Troczka-Pawelec, Katarzyna

Commentat. Math. 51, No. 1, 71-75 (2011).

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

Keywords:

subquadratic functions, semicontinuity; functional inequalities