Linear Algebra/Algebra Seminar

Speaker: Trung Hoa Dinh

Title: Some inequalities for operator $(p,h)$-convex functions.

Abstract: Let $p$ be a positive number and $h$ a function on $\mathbb{R}^+$ satisfying $h(xy) \ge h(x) h(y)$ for any $x, y \in \mathbb{R}$. A non-negative function $f$ on $K (\subset \mathbb{R}^+)$ is said to be $\it operator$ $(p,h)$-convex if 

In this talk, we study properties of $(p,h)$-convex functions and prove the Jensen, Hansen-Pedersen type inequalities for them. We also give some equivalent conditions for a function to become an operator $$(p,h)$-convex. In applications, we obtain Choi-Davis-Jensen type inequality for operator $(p,h)$-convex functions and a relation between operator $(p,h)$-convex functions with operator monotone functions.