On the Existence and Uniqueness of (N, λ -Periodic Solutions to a Class of Volterra Difference Equations

In this paper we introduce the class of (N, λ) -periodic vector-valued sequences and show several notable properties of this new class. This class includes periodic, anti-periodic, Bloch and unbounded sequences. Furthermore, we show the existence and uniqueness of (N, λ) -periodic solutions to the following class of Volterra difference equations with infinite delay: u(n+1)=α∑j=−∞na(n−j)u(j)+f(n,u(n)),n∈Z,α∈C, where the kernel a and the nonlinear term f satisfy suitable conditions. © 2019, The Author(s).