Abstract: We formulate initial value problems for delay difference equations in Banach spaces as fixed-point problems in sequence spaces. By choosing appropriate sequence spaces various types of attractivity can be described. This allows us to establish global attractivity by means of fixed-point results. Finally, we provide an application to delay integrodifference equations in the space of continuous functions over a compact domain.

Keywords: Delay difference equations, contractive difference equations, fixed-point theory, population dynamics, integrodifference equations, global attractivity

Full Text: PDF