new qualitative results to delay integro-differential equations

This work deals with various qualitative analyses of solutions of a certain delay integro-differential equation (dide). we prove here six new theorems including sufficient conditions, on uniformly stability (us), boundedness, asymptotically stability (as), exponentially stability (es), integrability and instability of solutions, respectively. by defining a suitable lyapunov function (lf) and using the razumikhin method (rm), the proofs of the theorems are provided. we gave two examples to demonstrate applications of the established new conditions.