摘要：In this paper we introduce the class of ( N , λ ) $(N,\lambda )$ -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 ) $(N, \lambda )$ -periodic solutions to the following class of Volterra difference equations with infinite delay: u ( n + 1 ) = α ∑ j = − ∞ n a ( n − j ) u ( j ) + f ( n , u ( n ) ) , n ∈ Z , α ∈ C , $$ u(n+1)=\alpha \sum_{j=-\infty }^{n}a(n-j)u(j)+f \bigl(n,u(n) \bigr), \quad n \in \mathbb{Z}, \alpha \in \mathbb{C}, $$ where the kernel a and the nonlinear term f satisfy suitable conditions.
关键词：Discrete periodic functions ; Periodic functions of the second kind ; \((N; \lambda )\) -periodic discrete functions ; Volterra difference equations
