Asymptotically Almost Periodic Solutions Of Volterra Difference Equations And Research On Almost Periodic Type Sequences

In this thesis, we discuss the existence of asymptotically almost periodic solu-tions to a class of Volterra-type difference equations and establish some new proper-ties of almost periodic type sequences. The thesis is organized as follows.Chapter1, we introduce the development process and the research status of almost periodic functions.Chapter2, we introduce the definitions, properties and theorems of almost pe-riodic sequences.Chapter3, we establish a compactness criterion for the sets of asymptotically almost periodic sequences. Then, by Schauder’s fixed point theorem, we present an existence theorem for an asymptotically almost periodic solution to the Volterra-type difference equation:Chapter4, we obtain some new properties and two characterization theorems for pseudo almost periodic sequences.