Introduction/purpose: In this article, the author’s goal is to seek to obtain new inequalities of the Berezin type. Methods: The methods used are standard for operator theory. Results: Various inequalities of the type given by Huban et al. and Erkan have been obtained. Conclusions: In addition to obtaining various inequalities of the form given by Huban et al. and Erkan in particular, the authors sharpened the inequalities related to the Berezin norm.