On locally subadditive functions

Abstract

We define locally (on $C\subset R^2$) subadditive functions $f$, $f\:C\to R$, by $$f(x_1+x_2,y_1+y_2)\leq f(x_1,y_1)+f(x_2,y_2),\quad(x_1,y_1),(x_2,y_2)ın C,$$ where $C$ is some cone in $R^2$. The purpose of the paper is to find explicit form of such functions.