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Doss ρ -Almost Periodic Type Functions in R n

Author

Listed:
  • Marko Kostić

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

  • Vladimir E. Fedorov

    (Mathematical Analysis Department, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia
    Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av., 76, 454080 Chelyabinsk, Russia)

Abstract

In this paper, we investigate various classes of multi-dimensional Doss ρ -almost periodic type functions of the form F : Λ × X → Y , where n ∈ N , ∅ ≠ Λ ⊆ R n , X and Y are complex Banach spaces, and ρ is a binary relation on Y . We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss ρ -almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss ρ -almost periodic type functions with ( ω , c ) -periodic functions and Weyl- ρ -almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.

Suggested Citation

  • Marko Kostić & Wei-Shih Du & Vladimir E. Fedorov, 2021. "Doss ρ -Almost Periodic Type Functions in R n," Mathematics, MDPI, vol. 9(21), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2825-:d:673820
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    References listed on IDEAS

    as
    1. Marko Kostić & Wei-Shih Du, 2020. "Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
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