Asymptotically Weyl almost periodic functions in Lebesgue spaces with variable exponents

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.

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Stepanov-Like Pseudo-Almost Periodic Functions in Lebesgue Spaces with Variable Exponents L p(x)

Springer Proceedings in Mathematics & Statistics - New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health) ◽

10.1007/978-3-319-07755-0_13 ◽

2014 ◽

pp. 295-314 ◽

Cited By ~ 1

Author(s):

Toka Diagana ◽

Mohamed Zitane

Keyword(s):

Almost Periodic Functions ◽

Variable Exponents ◽

Almost Periodic ◽

Periodic Functions ◽

Lebesgue Spaces ◽

Pseudo Almost Periodic Functions ◽

Pseudo Almost Periodic

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Almost periodic and asymptotically almost periodic type functions in Lebesgue spaces with variable exponents Lp(x)

Filomat ◽

10.2298/fil2005629d ◽

2020 ◽

Vol 34 (5) ◽

pp. 1629-1644

Author(s):

Toka Diagana ◽

Marko Kostic

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Almost Periodic Functions ◽

Important Class ◽

Variable Exponents ◽

Almost Periodic ◽

Periodic Functions ◽

Lebesgue Spaces ◽

Asymptotically Almost Periodic

In this paper we introduce and analyze an important class of (asymptotically) Stepanov almost periodic functions in the Lebesgue spaces with variable exponents, which generalizes in a natural fashion all the (asymptotically) almost periodic functions. We then make extensive use of these new functions to study some abstract Volterra integro-differential equations in Banach spaces including multi-valued ones.

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Doss ρ-Almost Periodic Type Functions in Rn

Mathematics ◽

10.3390/math9212825 ◽

2021 ◽

Vol 9 (21) ◽

pp. 2825

Author(s):

Marko Kostić ◽

Wei-Shih Du ◽

Vladimir E. Fedorov

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Banach Spaces ◽

Binary Relation ◽

General Setting ◽

Translation Invariance ◽

Variable Exponents ◽

Almost Periodic ◽

Periodic Functions ◽

Lebesgue Spaces

In this paper, we investigate various classes of multi-dimensional Doss ρ-almost periodic type functions of the form F:Λ×X→Y, where n∈N, ∅≠Λ⊆Rn,X and Y are complex Banach spaces, and ρ is a binary relation on Y. We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss ρ-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss ρ-almost periodic type functions with (ω,c)-periodic functions and Weyl-ρ-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.

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