Asymptotic Behavior of Mild Solutions for a Class of Abstract Nonlinear Difference Equations of Convolution Type

We prove the existence and uniqueness of a weighted pseudo asymptotically mild solution to the following class of abstract semilinear difference equations: u(n+1)=A∑k=−∞na(n−k)u(k+1)+∑k=−∞nb(n−k)f(k,u(k)),n∈Z, where A is the generator of a resolvent sequence {S(n)}n∈N0 of bounded and linear operators defined in a Banach space X, the sequences a, b are complex-valued, and f∈ l1(Z× X, X). © 2019, The Author(s).