Some results on Kwong functions and related inequalities

We investigate some relations between Kwong functions and operator monotone functions. As an application, we present an arithmetic-geometric mean type inequality by showing that for two continuous functions f, g on (0,∞) such that h(t)=f(t)g(t) is a Kwong function and f(t)g(t)⩽t, any positive matrices A, B and any matrix X, it holds that|||f(A)Xg(B)+g(A)Xf(B)|||⩽|||AX+XB||| for each unitarily invariant norm |||.|||.