It is shown, among other inequalities, that if \(A, B, X_1, X_2\) are n by n complex matrices where A, B are positive semidefinite matrices, if g is a nonnegative increasing concave function on \([0, \infty )\) and \(p,q\in (0,1)\) , then \(\begin{aligned} |||g(|(X_2AX_1 + X_1BX_2) \oplus 0|)||| \le |||N \oplus K||| \end{aligned}\) for every unitarily invariant norm, where \(N=g(N_{1})+g(|Z^*|),~~K=g(N_2)+g(|Z|),\) \(N_{1}=\frac{1}{2}(A^{p}|X_2|^{2}A^{p}+A^{1-p}|X_1^{*}|^{2}A^{1-p}),\) \( N_2=\frac{1}{2}(B^{1-q}|X_1|^{2}B^{1-q}+B^{q}|X_2^{*}|^{2}B^{q}) \) and \( Z=\frac{1}{2}(A^{p}X_2^{*}X_1B^{1-q}+A^{1-p}X_1X_2^{*}B^{q}). \) Several related singular value inequalities and norm inequalities are also given.
