On Majorization for Matrices

Khan, M. Adil, et al. "On Majorization for Matrices." Mathematica Balkanica New Series 27.1-2 (2013): 3-19. <http://eudml.org/doc/281438>.

@article{Khan2013,
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.},
author = {Khan, M. Adil, Latif, Naveed, Pecaric, J., Peric, I.},
journal = {Mathematica Balkanica New Series},
keywords = {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},
language = {eng},
number = {1-2},
pages = {3-19},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {On Majorization for Matrices},
url = {http://eudml.org/doc/281438},
volume = {27},
year = {2013},
}

TY - JOUR
AU - Khan, M. Adil
AU - Latif, Naveed
AU - Pecaric, J.
AU - Peric, I.
TI - On Majorization for Matrices
JO - Mathematica Balkanica New Series
PY - 2013
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 27
IS - 1-2
SP - 3
EP - 19
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/281438
ER -