Almost-Periodic Functions in Banach Spaces

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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A Remark on Integration of Almost-Periodic Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1970-050-3 ◽

1970 ◽

Vol 13 (2) ◽

pp. 249-251

Author(s):

S. Zaidman

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Almost Periodic Functions ◽

Almost Periodic ◽

Periodic Functions

A result proved by Favard for scalar-valued almost-periodic functions has an immediate extension to Banach space valued functions (see [2] and [3] for explicit details).The result says that integrals of almost-periodic functions whose 'spectrum' is at positive distance from 0 are again almost-periodic. Our aim here is to indicate a more general formulation of this result using strongly almost-periodic oneparameter groups of operators in Banach spaces.

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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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(&omega,c)- PSEUDO ALMOST PERIODIC FUNCTIONS, (&omega,c)- PSEUDO ALMOST AUTOMORPHIC FUNCTIONS AND APPLICATIONS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi200421014k ◽

2021 ◽

pp. 165

Author(s):

Mohammed Taha Khalladi ◽

Marko Kostić ◽

Abdelkader Rahmani ◽

Daniel Velinov

Keyword(s):

Banach Spaces ◽

Almost Periodic Functions ◽

Almost Periodic ◽

Periodic Functions ◽

First Order ◽

Almost Automorphic Functions ◽

Pseudo Almost Periodic Functions ◽

Pseudo Almost Automorphic ◽

Pseudo Almost Periodic ◽

Automorphic Functions

In this paper, we introduce the classes of $(\omega, c)$-pseudo almost periodicfunctions and $(\omega, c)$-pseudo almost automorphicfunctions. These collections include $(\omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.

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