Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices

Recently, there have been many authors, who established a number of inequalities involving Khatri-Rao and Hadamard products of two positive matrices. In this paper, the results are established in the following three ways. First, we find generalization of the inequalities involving Khatri-Rao product using results given by Liu ( 1999), Mond and Pecaric ( 1997), Cao et al. ( 2002), Chollet ( 1997), and Visick ( 2000). Second, we recover and develop some results of Visick. Third, the results are extended to the case of Khatri-Rao product of any finite number of matrices. These results lead to inequalities involving Hadamard product, as a special case.