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A Set of Almost Automorphic Functions and Applications
UMR Espace-Dev, Université de Guyane, Cayenne, Guyane, France
Laboratoire MEMIAD, Université des Antilles, Pointe à Pitre, Guadeloupe, France
- 1 UMR Espace-Dev, Université de Guyane, Cayenne, Guyane, France
- 2 Laboratoire MEMIAD, Université des Antilles, Pointe à Pitre, Guadeloupe, France
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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.
KeywordsAlmost Automorphic FunctionsS-Almost Automorphic FunctionsDifferential Equation with Piecewise Constant Argument of Generalized Type
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