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 an unified extension of the
recent inequalities due to Choi [6], Lin [14] and Zhang et al. [5,19]. We
demonstrate the applications of a positive semidefinite 3×3 block
matrix, which motivates us to give a simple alternative proof of Dragomir's
inequality and Krein's inequality.Comment: 12 pages. This paper was originally written on Nov. 02, 2019;
Recently, we make a new revision. Any commennts are wellcom