The Berezin transform ̃ A of an operator A, acting on the reproducing kernel Hilbert space H = H(Θ) over some (non-empty) set Θ, is defined by ̃ A(λ) = ⟨Aˆk⟨Aˆ ⟨Aˆk λ , ˆ k λ ⟩ (λ ∈ Θ), wherê k λ = k λ ∥k λ ∥ is the normalized reproducing kernel of H. The Berezin number of an operator A is defined by ber(A) = sup λ∈Θ ∣ ̃ A(λ)∣ = sup λ∈Θ ∣⟨Aˆk∣⟨Aˆ ∣⟨Aˆk λ , ˆ k λ ⟩∣. In this paper, by using the definition of-generalized Euclidean Berezin number, we obtain some possible relations and inequalities. It is shown, among other inequalities, that if A i ∈ L(H(Θ)) (i = 1,. .. , n), then ber(A 1 , ..., An) ≤ −1 (n ∑ i=1 (ber(A i))) ≤ n ∑ i=1 ber(A i), in which ∶ [0, ∞) → [0, ∞) is a continuous increasing convex function such that (0) = 0.