  We present inequalities related to generalized matrix function for positive
semidefinite block matrices. We introduce partial generalized matrix functions
corresponding to partial traces, and then provide a unified extension of the
recent inequalities due to Lin [Electron. J. Linear Algebra 27 (2014) 821-826],
Zhang et al. [Linear Algebra Appl. 498 (2016) 99-105] and [Electron. J. Linear
Algebra 27 (2014) 332-341] and a result of Choi [Linear Algebra Appl. 532
(2017) 1-7]. Moreover, we demonstrate the application of a positive
semidefinite $3\times 3$ block matrix, which motivates us to give alternative
proofs of Dragomir's inequality and Krein's inequality.
