convex function Green function majorization for matrices positive semi-definite matrices exponential-convexity log-convexity Lypunov's inequality Dresher's inequality mean value theorems Cauchy means
Issue Date:
2013
Publisher:
Bulgarian Academy of Sciences - National Committee for Mathematics
Citation:
Mathematica Balkanica New Series, Vol. 27, Fasc 1-2 (2013), 3p-19p
Abstract:
In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.
