Singular values of convex functions of matrices

‎Let Ai,Bi,Xi,i=1,…,m, be n-by-n matrices such that ‎∑mi=1|Ai|² and ‎∑mi=1|Bi|² are nonzero matrices and each Xi is‎ ‎positive semidefinite‎. ‎It is shown that if f is a nonnegative increasing ‎convex function on [0,∞) satisfying f(0)‎‎=0‎, ‎then 2sj (f( |Σ^m_i=1 Ai*XiBi|/√||∑^m_i |Ai|² || ||∑^m_i|Bi|²||)) for j = 1,..., n. Applications of our results are given.