Matrix Hermite-Hadamard type inequalities

Details Matrix Hermite-Hadamard type inequalities Matrix Hermite-Hadamard type inequalities

2012-03-23

arxiv.org/abs/1203.5300v1

Mathematics

Functional Analysis

13 pages, to appear in Houston J. Math

Scientific paper

We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex functions. We also present some applications. Finally we obtain an Hermite-Hadamard inequality for operator convex functions, positive linear maps and operators acting on Hilbert spaces.

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