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Dimbour, W. and Manou-Abi, S. (2018) Asymptotically ω-Periodic Function in the Stepanov Sense and Its Applications for an Advanced Differential Equation with Piecewise Constant Argument in a Banach Space. Mediterranean Journal of Mathematics, 15, Article No. 25.
https://doi.org/10.1007/s00009-018-1071-6

has been cited by the following article:

• 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.