✦ LIBER ✦

Convex functions and mean value inequalities

✍ Scribed by Hartman, Philip

Book ID: 121701219
Publisher: Duke University Press
Year: 1972
Tongue: English
Weight: 840 KB
Volume: 39
Category: Article
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-72-03942-7

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Let f be a convex function defined on an interval I , 0 α 1 and A, B n × n complex Hermitian matrices with spectrum in I. We prove that the eigenvalues of f (αA + (1α)B) are weakly majorized by the eigenvalues of αf (A) + (1α)f (B). Further if f is log convex we prove that the eigenvalues of f (αA +