A Bishop-Phelps-Bollobas theorem for disc algebra

Let $\mathbb{D}$ represent the open unit disc in $\mathbb{C}$. Denote by $A(\mathbb{D})$ the disc algebra, and $\mathcal{B}(X,A(\mathbb{D}))$ the Banach space of all bounded linear operators from a Banach space $X$ into $A(\mathbb{D})$. We prove that, under the assumption of equicontinuity at a point in $\mathrm{\partial }\mathbb{D}$, the Bishop-Phelps-Bollobás property holds for $\mathcal{B}(X,A(\mathbb{D}))$.