Multi-dimensional besicovitch almost periodic type functions and applications

Kostić, Marko

doi:10.3934/cpaa.2022141

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Almost Periodic Then the Following Holds1

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2023

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Cited by 2 publications

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“…Before proceeding to the next section, we will only note that the statements of ( [28] Propositions 1 and 2) can be formulated in the discrete setting; cf. also ([17] Lemma 3.1), which can be formulated if one of the corresponding sequences b(•) or c(•) is vector-valued.…”

Section: Almost Periodic Then the Following Holdsmentioning

confidence: 99%

Generalized ρ-Almost Periodic Sequences and Applications

Kostić

Chaouchi

et al. 2023

Fractal Fract

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In this paper, we analyze the Bohr ρ-almost periodic type sequences and the generalized ρ-almost periodic type sequences of the form F:I×X→Y, where ∅≠I⊆Zn, X and Y are complex Banach spaces and ρ is a general binary relation on Y. We provide many structural results, observations and open problems about the introduced classes of ρ-almost periodic sequences. Certain applications of the established theoretical results to the abstract Volterra integro-difference equations are also given.

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Section: Almost Periodic Then the Following Holdsmentioning

confidence: 99%

Generalized ρ-Almost Periodic Sequences and Applications

Kostić

Chaouchi

et al. 2023

Fractal Fract

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Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions

Kostić

Velinov

2023

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In this paper, we introduce and systematically analyze the classes of (pre-)(B,ρ,(tk))-piecewise continuous almost periodic functions and (pre-)(B,ρ,(tk))-piecewise continuous uniformly recurrent functions with values in complex Banach spaces. We weaken substantially, or remove completely, the assumption that the sequence (tk) of possible first kind discontinuities of the function under consideration is a Wexler sequence (in order to achieve these aims, we use certain results about Stepanov almost periodic type functions). We provide many applications in the analysis of the existence and uniqueness of almost periodic type solutions for various classes of the abstract impulsive Volterra integro-differential inclusions.

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Multi-dimensional besicovitch almost periodic type functions and applications

Cited by 2 publications

References 30 publications

Generalized ρ-Almost Periodic Sequences and Applications

Generalized ρ-Almost Periodic Sequences and Applications

Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions

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