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.
Highlights
Introduction and PreliminariesThe class of almost-periodic functions was introduced by a Danish mathematician HaraldBohr [1,2,3], (1924–1926), the younger brother of the Nobel Prize-winning physicist Niels Bohr, and later generalized by many others.The theory of almost-periodic functions is still a very active field of investigations of numerous authors, full of open problems, conjectures, hypotheses and possibilities for further expansions.The notion of Stepanov almost-periodicity and the notion ofStepanov almost automorphicity in Lebesgue spaces with variable exponents have been introduced in the papers [11,12] by Diagana and Zitane
The main aim of this paper is to continue the analysis raised in the above-mentioned papers by introducing and investigating the classes of Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and
A great number of composition principles established for Stepanov p( x )-almost-periodic functions can be extended for Stepanov p( x )-uniformly recurrent functions
Summary
The class of almost-periodic functions was introduced by a Danish mathematician Harald. Stepanov almost automorphicity in Lebesgue spaces with variable exponents have been introduced in the papers [11,12] by Diagana and Zitane. In [15,16,17], we have recently analyzed the classes of (Stepanov) uniformly recurrent functions and several various classes of (asymptotically) Weyl almost-periodic functions in Lebesgue spaces with variable exponents. Doss almost-periodic functions in Lebesgue spaces with variable exponents. For additional details upon Lebesgue spaces with variable exponents L p( x) , we refer the reader to [11,12,18]
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