generalize‎ ‎the celebrated Jensen inequality‎ ‎for continuous $m$-convex functions and Hilbert space operators‎ ‎and then use suitable weight functions to give some weighted refinements of it‎.

‎Introducing the notion of operator $m$-convexity‎, ‎we...

We present a Bellman inequality involving operator means for

operators acting on a Hilbert space. We also give some Bellman

inequalities concerning sesquilinear forms. Finally, we refine the

Jensen's ...

an operator version of the

Jensen inequality for P-class functions. Introducing operator (mid) P-class functions, we

present some characterizations for such functions....

A Jensen inequality for some unital n-tuples of positive linear maps,

n-tuples of self-adjoint operators and continuous Q-class functions under

certain conditions is proved....

Jensen inequality in the content of Hilbert

C∗-modules, another extension of Hua’s inequality is obtained.We

also present an operator Hua’s inequality, which is equivalent to

operator convexity of given continuous real function....