Berezin Yarıçapı İçin Diğer Eşitsizlikler.

Functional Hilbert spaces are encountered in a variety of fields, including statistics, approximation theory, group representation theory, and so on. Smooth functions are associated with operators on Hilbert spaces of analytic functions through the Berezin transform defined by functional Hilbert space. We present new inequalities for the Berezin norm and Berezin number of limited linear operators defined on a functional Hilbert space in this study. We discovered various inequalities and their features in some papers to characterize the Berezin number and the Berezin norm. This article's originality or novelty consists of fresh Berezin number estimations for two operators. These estimates improve on the upper bounds of the Berezin numbers found in previous studies. The inequality given by El-Haddad and Kittaneh ([10]) is then improved and generalized after that. The concepts and approaches offered in this paper may serve as a starting point for future research in this field. [ABSTRACT FROM AUTHOR]