Inequalities Involving Berezin Norm and Berezin Number

We obtain new inequalities involving Berezin norm and number of bounded linear operators defined on a reproducing kernel Hilbert space $${\mathscr {H}}.$$ Among many obtained here, it is shown that if A positive operator {H}}$$ , then $$\Vert A\Vert _{ber}={{{\textbf {ber}}}}(A)$$ where _{ber}$$ $${{{\textbf are the A, respectively. In contrast to numerical radius, this equality does not hold for selfadjoint operators, which highlights necessity studying independently.