Monotone iterative technique for addressing impulsive integro-differential equations in Banach spaces

In this paper, we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of solutions for the initial value problem of the impulsive integro-differential equation of Volterra type in a Banach space EE{u′(t)=f(t,u(t),Tu(t)),t∈J,t≠tk,Δu|t=tk=Ik(u(tk)),k=1,2,…,m,u(0)=x0, where f∈C(J×E×E,E)f∈C(J×E×E,E), J=[0,a]J=[0,a], 0