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In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x^{\text{'}}\left(t\right)+Ax\left(t\right)=f(t,x\left(t\right),{\int }_{t₀}^{t}k(t,s,x\left(s\right))ds)$, x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator ${T\left(t\right)}_{t>0}$ on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.