Asymptotic almost periodicity and motions of semigroups of operators

Ruess, Wolfgang M.; Summers, W. H.

doi:10.1016/0024-3795(86)90325-3

Cited by 28 publications

(22 citation statements)

References 14 publications

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“…The following theorem is motivated by some pioneering results of Ruess and Summers concerning integration of asymptotically almost periodic functions [24]. (v) For every ∈ N, we have…”

Section: 10(vi)])mentioning

confidence: 99%

“…A great number of important phenomena in electromagnetics, acoustics, viscoelasticity, aerodynamics, electrochemistry, and cosmology are well described and modelled by fractional differential equations. For basic information about fractional calculus and nondegenerate fractional differential equations, one may refer, for example, to [11,12,[20][21][22][23][24][25] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

N’Guérékata

Kostić

2018

Abstract and Applied Analysis

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“…The following theorem is motivated by some pioneering results of Ruess and Summers concerning integration of asymptotically almost periodic functions [24]. (v) For every ∈ N, we have…”

Section: 10(vi)])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

N’Guérékata

Kostić

2018

Abstract and Applied Analysis

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“…(iii) Asymptotic Bohr-almost periodicity is strictly weaker than Bohr-almost periodicity, as shows the following example provided by Ruess and Summers [16]:…”

mentioning

confidence: 77%

“…If E is a vector space, a function x : R → E is asymptotically Bohr-almost periodic iff it has the form x = y + z, where y is Bohr-almost periodic and z is a continuous function with lim ±∞ z = 0, see e.g. [16].…”

mentioning

confidence: 99%

Bochner-Almost Periodicity for Stochastic Processes

Bedouhene

Mellah

Fitte

2012

Stochastic Analysis and Applications

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We compare several notions of almost periodicity for continuous processes defined on the time interval I = R or I = [0, +∞) with values in a separable Banach space E (or more generally a separable completely regular topological space): almost periodicity in distribution, in probability, in quadratic mean, almost sure almost periodicity, almost equi-almost periodicity. In the deterministic case, all these notions reduce to Bochner-almost periodicity, which is equivalent to Bohr-almost periodicity when I = R, and to asymptotic Bohr-almost periodicity when I = [0, +∞).

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“…It is well known that (see Ruess, Summers, and Vũ Quôc Phóng [27,[31][32][33]), for any function f ∈ C([0, ∞) : X), the following statements are equivalent:…”

Section: Asymptotically Almost Periodic Functionsmentioning

confidence: 99%

Almost periodic and asymptotically almost periodic functions: part I

Lassoued

Shah

2018

Adv Differ Equ

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In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions. We also recollect some basic results regarding equi-Weyl-almost periodic functions and Weyl-almost periodic functions. The class of asymptotically Weyl-almost periodic functions, introduced in this work, seems to be not considered elsewhere even in the scalar-valued case. We actually introduce eight new classes of asymptotically almost periodic functions and analyze relations between them. In order to make a picture as complete and clear as possible, several illustrating examples and counter-examples are given. It is worth noting that the topics dealt with in this paper seem to be of an intrinsic connection with the problem of existence and uniqueness of solutions of differential and difference equations, in both determinist and stochastic cases. MSC: 42A75

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Asymptotic almost periodicity and motions of semigroups of operators

Cited by 28 publications

References 14 publications

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Bochner-Almost Periodicity for Stochastic Processes

Almost periodic and asymptotically almost periodic functions: part I

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