Refinements of Kantorovich type, Schwarz and Berezin number inequalities

In this article, we use Kantorovich and Kantorovich type inequalities in order to prove some new Berezin number inequalities. Also, by using a re_nement of the classical Schwarz inequality, we prove Berezin number inequalities for powers of f(A), where A is self-adjoint operator on the Hardy space H2(D) and f is a positive continuous function. Some related questions are also discussed.peerReviewe