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