An extension theorem for a Matkowski–Sutô problem
An extension theorem for a Matkowski–Sutô problem
Let $I$ be an interval, $0<\lambda <1$ be a fixed constant and $A(x,y)=\lambda x+(1-\lambda ) y,\, x,y \in I,$ be the weighted arithmetic mean on $I$. A pair of strict means $M$ and $N$ is complementary with respect to $A$ if $A(M(x,y),N(x,y))=A(x,y)$ fo