Author(s)

William Dimbour¹, Vincent Valmorin²

¹UMR Espace-Dev, Université de Guyane, Cayenne, Guyane, France.
²Laboratoire MEMIAD, Université des Antilles, Pointe à Pitre, Guadeloupe, France.

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.

Almost Automorphic Functions, S-Almost Automorphic Functions, Differential Equation with Piecewise Constant Argument of Generalized Type

Dimbour, W. and Valmorin, V. (2024) A Set of Almost Automorphic Functions and Applications. Applied Mathematics, 15, 9-21. doi: 10.4236/am.2024.151002.