Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

Abstract

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

Keywords

• stepanov uniformly recurrent functions
• doss uniformly recurrent functions
• doss almost-periodic functions
• lebesgue spaces with variable exponents