© 2022 Himia, Fizika ta Tehnologia Poverhni. All rights reserved.The Berezin transform Ae and the Berezin radius of an operator A on the reproducing kernel Hilbert space over some set Qwith normalized reproducing kernel kη := kKKηηk are defined, respectively, by Ae(η) = hAkη, kηi, η ∈ Qand ber(A):= supη∈Q|||Ae(η) |||. A simple comparison of these properties produces the inequalities 14 kA∗A + AA∗k ≤ ber2 (A) ≤ 21 kA∗A + AA∗k. In this research, we investigate other inequalities that are related to them. In particular, for A ∈ L(H(Q)) we prove that ber2 (A) ≤ 12 kA∗A + AA∗kber − 14 ηinf ∈Q ((|fA|(η)) − (|gA∗|(η) ))2