TITLE:
A Set of Almost Automorphic Functions and Applications
AUTHORS:
William Dimbour, Vincent Valmorin
KEYWORDS:
Almost Automorphic Functions, S-Almost Automorphic Functions, Differential Equation with Piecewise Constant Argument of Generalized Type
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.1,
January
19,
2024
ABSTRACT: For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.