Abstract
A typical result given in this paper is as follows: For an N X N positive definite Hermitian matrix A and for any vector x ϵ C , we obtain the inequality (expx) ∗( expA -1) -1 (expx)⩽ exp(x ∗Ax) , where, for x = ( x 1, x 2,…, x N ) T , expx = (exp x 1, exp x 2,…,exp x N ) T and for A=‖ a νμ ‖, exp A=‖(exp a νμ )‖.We deal with inequalities of this type in a more general situation by using the theory of reproducing kernels.
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