Several new inequalities on operator means of non-negative maps and Khatri–Rao products of positive definite matrices

In this paper, we provide some interested operator inequalities related with non-negative linear maps by means of concavity and convexity structure, and also establish some new attractive inequalities for the Khatri–Rao products of two or more positive definite matrices. These results lead to inequalities for Hadamard product and Ando’s and a-power geometric means, as a special case.