Midconvex sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $midconvex$ if for every $x,y\in X$ the set $\frac{x+y}{2}=\{z\in G:2z=x+y\}$ is a subset of $X$. We prove that a subset $X$ of an Abel…