Abstract
Let p be a positive number and h a function on satisfying for any . A non-negative continuous function f on is said to be operator (p, h)-convex ifholds for all positive semidefinite matrices A, B of order n with spectra in K, and for any . In this paper, we study properties of operator (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.
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