INEQUALITIES FOR SEMI-CONVEX MATRIX FUNCTIONS

Authors
MOND B PECARIC JE
Citation
B. Mond et Je. Pecaric, INEQUALITIES FOR SEMI-CONVEX MATRIX FUNCTIONS, Journal of mathematical analysis and applications, 185(2), 1994, pp. 367-377
Citations number
4
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
185
Issue
2
Year of publication
1994
Pages
367 - 377
Database
ISI
SICI code
0022-247X(1994)185:2<367:IFSMF>2.0.ZU;2-K
Abstract
f defined on the set T of matrices with values in the set of matrices is said to be semi-convex if X, Y is-an-element-of T, X less-than-or-e qual-to Y implies that lambdaX + (1 - lambda) Y is-an-element-of T, 0 < lambda < 1, and f(lambdaX + (1 - lambda) Y) less-than-or-equal-to la mbdaf(X) + (1 - lambda)f(Y). Here X less-than-or-equal-to Y means that every element of Y - X is nonnegative. In this paper, a number of dif ferent inequalities are given for semi-convex functions of matrices. ( C) 1994 Academic Press, Inc.