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Weighted Ergodic Components in \({{\mathbb {R}}}^{n}\)

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Abstract

In this paper, we analyze various classes of weighted Stepanov ergodic spaces, weighted Weyl ergodic spaces and weighted pseudo-ergodic spaces in \({{\mathbb {R}}}^{n}\) with the help of results from the theory of Lebesgue spaces with variable exponents \(L^{p(x)}\). Several structural results of ours seem to be new even in the case of consideration of the constant exponents \(p(x)\equiv p\in [1,\infty ).\) We especially examine the Stepanov asymptotical almost periodicity at minus infinity and the Weyl asymptotical almost periodicity at minus infinity, providing also some interesting applications to the abstract Volterra integro-differential equations in Banach spaces.

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Acknowledgements

The authors would like to express their sincere gratitude to the referees for their careful reading of the manuscript and many valuable hints provided.

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Authors and Affiliations

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

    Marko Kostić

  2. Lab. de l’Energie et des Systèmes Intelligents, Khemis Miliana University, 44225, Khemis Miliana, Algeria

    Belkacem Chaouchi

  3. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 82444, Taiwan

    Wei-Shih Du

Authors
  1. Marko Kostić
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  2. Belkacem Chaouchi
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  3. Wei-Shih Du
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Correspondence to Marko Kostić.

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Communicated by Mohammad S. Moslehian.

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Marko Kostić is partially supported by Grant 451-03-68/2020/14/200156 of Ministry of Science and Technological Development, Republic of Serbia. Wei-Shih Du is partially supported by Grant no. MOST 107-2115-M-017-004-MY2 of the Ministry of Science and Technology of the Republic of China.

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Kostić, M., Chaouchi, B. & Du, WS. Weighted Ergodic Components in \({{\mathbb {R}}}^{n}\). Bull. Iran. Math. Soc. 48, 2221–2253 (2022). https://doi.org/10.1007/s41980-021-00597-5

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  • DOI: https://doi.org/10.1007/s41980-021-00597-5

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