Josep Pecaric

An extension of the generalised schur inequality

The well-known Schur inequality relates the sum of the squares of the absolute values of the eigenvalues of A to the elements of A . This was recently generalised to powers between one and two. Here we show that the inequality holds for powers between zero and two.

Inequalities with weights for powers of generalised inverses

Recently the authors extended to positive semi-definite matrices converses of matrix inequalities corresponding to ratios and differences of means and of Holders inequality. Here, further generalisations are given to the case of several vectors with appropriate weights.

The generalised Hadamard inequality, g -convexity and functional Stolarsky means

We explore the role of weighted functional Stolarsky means in providing bounds in generalised Hadamard-type inequalities for g -convex functions. Refinements are given for Levinsons inequality and the generalised Hadamard inequality. Applications are made to multivariate weighted functional Stolarsky means.

Bounds on Entropy Measures for Mixed Populations

We derive a number of bounds relating entropy measures for a mixed population to parameters of the n constituent populations. The results extend some recent studies of Dragomir and Goh for the two-population case and are tighter than those given by them for the case n = 2.