Quasi-sum representation for an \(m\)-place function

Abstract. Aczél, in his book, reported on the associativity equation $$ F(F(x,y),z)=F(x,F(y,z)) $$ on a real interval. Conditions leading to the quasi-sum representation $$ F(x,y)=f(f^{-1}(x)+f^{-1}(y)) $$ were obtained. We expand on this and obtain results for an \(m\)-place function.