Stability of an abstract system with infinite history

This work is concerned with stabilization of an abstract linear dissipative integrodiffrential equation with infinite memory modeling linear viscoelasticity where the relaxation function satisfies $ g’(t)\leq -\xi(t)g^p(t), \forall t\geq 0, 1\leq p<\frac{3}{2}$. Our result improves earlier results in the literature.