Lebesgue Regularity for Nonlocal Time-Discrete Equations with Delays

In this work we provide a new and effective characterization for the existence and uniqueness of solutions for nonlocal time-discrete equations with delays, in the setting of vector-valued Lebesgue spaces of sequences. This characterization is given solely in terms of the R-boundedness of the data of the problem, and in the context of the class of UMD Banach spaces. © 2018 Diogenes Co., Sofia 2018.