This work aims to introduce a new Buzano-type inequality that integrates and unifies several well-established results from the literature. As a consequence, we present novel numerical radius bounds for operators in semi-Hilbertian spaces. For example, it is proven that for \(T \in \mathcal {L}_{A}(\mathcal {H})\) and a mapping \(\chi : [0,1]\subset J \rightarrow [\frac{1}{4},1]\) , \(\begin{aligned} \omega _{A}^{4}(T) \leqslant \frac{\chi (\lambda )}{4}\left\| T^{\sharp _{A}} T+TT^{\sharp _{A}}\right\| _{A}^{2}+\frac{(1-\chi (\lambda ))}{2}\left\| T^{\sharp _{A}} T+T T^{\sharp _{A}}\right\| _{A} \omega _{A}\left( T^{2}\right) . \end{aligned}\) Additionally, we establish several bounds for the \(\mathbb {A}\) -numerical radii of \(2 \times 2\) operator matrices. Our results extend and improve certain well-established inequalities from existing literature.
