On the Composition of Homogeneous Quasi-Arithmetic Means

Let f, c , g , b : 0,`.ªR, strictly monotonic and continuous functions, be the generators of the positively homogeneous quasi-arithmetic means M , M , M , f c g and M . The main result gives full characterizations of the functions f, c , g , and b b such that M M x,y.,M x,y..sM x,y., x,y)0