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Mathématiques   > Accueil   > Avancées en Mathématiques Pures et Appliquées   > Numéro 4 (Septembre 2023)   > Article

Les fonctions de Weyl presque automorphes et applications

Weyl almost automorphic functions and applications


M. Kostić
University of Novi Sad
Serbia



Publié le 8 septembre 2023   DOI : 10.21494/ISTE.OP.2023.0998

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Abstract

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In this paper, we reconsider the notion of a Weyl p-almost automorphic function introduced by S. Abbas [1] in 2012 and propose several new ways for introduction of the class of Weyl p-almost automorphic functions (1 ⩽ p < ∞). We first analyze the introduced classes of Weyl p-almost automorphic functions of type 1, jointly Weyl p-almost automorphic functions and Weyl p-almost automorphic functions of type 2 in the one-dimensional setting. After that, we introduce and analyze generalizations of these classes in the multi-dimensional setting, working with general Lebesgue spaces with variable exponents. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations.

In this paper, we reconsider the notion of a Weyl p-almost automorphic function introduced by S. Abbas [1] in 2012 and propose several new ways for introduction of the class of Weyl p-almost automorphic functions (1 ⩽ p < ∞). We first analyze the introduced classes of Weyl p-almost automorphic functions of type 1, jointly Weyl p-almost automorphic functions and Weyl p-almost automorphic functions of type 2 in the one-dimensional setting. After that, we introduce and analyze generalizations of these classes in the multi-dimensional setting, working with general Lebesgue spaces with variable exponents. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations.

Weyl almost automorphic functions Weyl almost periodic functions double sequences Lebesgue spaces with variable exponents abstract Volterra integro-differential equations

Weyl almost automorphic functions Weyl almost periodic functions double sequences Lebesgue spaces with variable exponents abstract Volterra integro-differential equations