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Generalized Almost-Periodicity in Lebesgue Spaces with Variable Exponents

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Open AccessArticle

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

by Marko Kostić 1 and Wei-Shih Du 2,*
1
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
2
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1052; https://doi.org/10.3390/math8071052
Received: 4 June 2020 / Revised: 24 June 2020 / Accepted: 25 June 2020 / Published: 30 June 2020
(This article belongs to the Special Issue Fixed Point Theory and Dynamical Systems with Applications)
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 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
MDPI and ACS Style

Kostić, M.; Du, W.-S. Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II. Mathematics 2020, 8, 1052.

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