A-Berezin radius distance and A-Berezin norm distance are presented in this study. Furthermore, by employing the notions of A-Berezin radius distance and A-Berezin norm distance, we find A-Berezin radius inequalities of the product and commutator of functional Hilbert space operators. Moreover, we generalize the A-Berezin radius distance. Finally, we prove the theorem pertaining to the A-Berezin radius distance. To recapitulate, the A-Berezin number∣ of operator V on L (H(Θ)) is defined by the following ∣∣∣〈 〉 special type of quadratic form: berA (V) = supη∈ΘV̂kη,̂kη ∣ ∣, η ∈ Θ, whereˆkη is the normalized reproducing kernel on H and a semi-inner product on H, denoted as ⟨Vˆkη,ˆkη ⟩A:= ⟨AVˆkη,ˆkη ⟩H, is induced by any positive operator A. A.