Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II

Abstract

In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost periodic type functions and generalized uniformly recurrent type functions. We also investigate the invariance of generalized almost periodicity and generalized uniform recurrence with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract fractional differential inclusions in Banach spaces.

Keywords

• Weyl uniformly recurrent functions with variable exponents
• quasi-asymptotically uniformly recurrent functions with variable exponents
• quasi-asymptotically almost periodic functions with variable exponents
• S-asymptotically ω-periodic functions with variable exponents
• Lebesgue spaces with variable exponents