Regularity of weakly subquadratic functions (Q549817)

Let \(G\) be a topological group and consider the collection of all real-valued functions \(f\) on \(G\) satisfying the functional inequality \[ f(x+y) + f(x-y) \leq 2f(x) + 2f(y)\;,\quad x,y\in G\;. \] The upper and lower hulls of such a collection of functions are studied, and some Bernstein-Doetsch type theorems are established.