We compute certain inequalities for B-Berezin radius of 2×2 operator matrices in the study that generalize and refine earlier inequalities. Furthermore, we construct A-Berezin radius inequalities of operators in BA,Υ(H) that improve on the current inequalities in Huban (Turk J Math 46(1):189–206, 2022). In addition, we establish A-Berezin radius bounds for sum of product of operators in BA,Υ(H), which improve on the previous bounds.