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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Forthcoming papers   > Article

[FORTHCOMING] Weyl almost automorphic functions and applications

[FORTHCOMING] Les fonctions de Weyl presque automorphes et applications


M. Kostić
University of Novi Sad
Serbia



Published on 15 March 2023   DOI :

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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