Inequalities forTϕ-convex functions
✍ Scribed by Shi-jie Li; Ling-zhi Zhao; Gang-song Leng
- Book ID
- 107482468
- Publisher
- Chinese Electronic Periodical Services
- Year
- 2007
- Tongue
- English
- Weight
- 167 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1007-6417
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Many converses of Jensen's inequality for convex functions can be found in the literature. Here we give matrix versions, with matrix weights, of these inequalities. Some applications to the Hadamard product of matrices are also given. ᮊ 1997
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 +