Generalized <i>ρ</i>-Almost Periodic Sequences and Applications

Abstract

In this paper, we analyze the Bohr ρ-almost periodic type sequences and the generalized ρ-almost periodic type sequences of the form F:I×X→Y, where ∅≠I⊆Zn, X and Y are complex Banach spaces and ρ is a general binary relation on Y. We provide many structural results, observations and open problems about the introduced classes of ρ-almost periodic sequences. Certain applications of the established theoretical results to the abstract Volterra integro-difference equations are also given.

Keywords

• generalized <i>ρ</i>-almost periodic sequence
• generalized <i>ρ</i>-almost periodic function
• abstract Volterra integro-difference equation
• abstract impulsive Volterra integro-differential equation
• Banach space