In this article, we study the ccs-Daugavet, ccs- \(\Delta \) , super-Daugavet, super- \(\Delta \) , Daugavet, \(\Delta \) , and \(\nabla \) points in the unit balls of vector-valued function spaces \(C_0(L, X)\) , A(K, X), \(L_\infty (\mu , X)\) , and \(L_1(\mu , X)\) . To partially or fully characterize these diametral points, we first provide improvements of several stability results under \(\oplus _\infty \) and \(\oplus _1\) -sums shown in the literature. For complex Banach spaces, \(\nabla \) points are identical to Daugavet points, and so the study of \(\nabla \) points only makes sense when a Banach space is real. Consequently, we obtain that the seven notions of diametral points are equivalent for \(L_\infty (\mu )\) and uniform algebra when K is infinite.
