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In this paper we use a monotone iterative technique in the presence of the lower and upper solutions to discuss the existence of mild solutions for a class of semilinear impulsive integro-differential evolution equations of Volterra type with nonlocal conditions in a Banach space $E$ $$\left\{\begin{array}{c}{u}^{\text{'}}\left(t\right)+Au\left(t\right)=f(t,u\left(t\right),Gu\left(t\right)),t\in J,t\ne t_k{,\Delta u|}_{t=t_k}=u\left(t_k^{+}\right)-u\left(t_k^{-}\right)=I_k\left(u\left(t_k\right)\right),k=1,2,\cdots ,m,u\left(0\right)=g\left(u\right)+x_0,\hfill \end{array}\right.$$ where $A:D\left(A\right)\subset E\to E$ is a closed linear operator and $-A$ generates a strongly continuous semigroup $T\left(t\right)$ $(t\ge 0)$ on $E$, $f\in C(J\times E\times E,E)$, $J=[0,a]$, $0<t_1<t_2<\cdots <t_m<a$, $I_k\in C(E,E)$, $k=1,2,\cdots ,m$, and $g$ constitutes a nonlocal condition. Under suitable monotonicity conditions...

This paper discusses the existence of mild solutions for a class of semilinear fractional evolution equations with nonlocal initial conditions in an arbitrary Banach space. We assume that the linear part generates an equicontinuous semigroup, and the nonlinear part satisfies noncompactness measure conditions and appropriate growth conditions. An example to illustrate the applications of the abstract result is also given.