On inequalities for A-Berezin radius of operators

We compute certain inequalities for B-Berezin radius of \(2\times 2\) $2\times 2$ operator matrices in the study that generalize and refine earlier inequalities. Furthermore, we construct A-Berezin radius inequalities of operators in \(\mathbb {B}_{A,\Upsilon }(\mathcal {H})\) ${\mathbb{B}}_{A,\mathrm{{\rm Y}}}(\mathcal{H})$ 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 \(\mathbb {B}_{A,\Upsilon } (\mathcal {H}),\) ${\mathbb{B}}_{A,\mathrm{{\rm Y}}}(\mathcal{H}),$ which improve on the previous bounds.