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Modular Geometric Properties in Variable Exponent Spaces

Author

Listed:
  • Mohamed A. Khamsi

    (Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates)

  • Osvaldo D. Méndez

    (Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA)

  • Simeon Reich

    (Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 3200003, Israel)

Abstract

Much has been written on variable exponent spaces in recent years. Most of the literature deals with the normed space structure of such spaces. However, because of the variability of the exponent, the underlying modular structure of these spaces is radically different from that induced by the norm. In this article, we focus our attention on the progress made toward the study of the modular structure of the sequence Lebesgue spaces of variable exponents. In particular, we present a survey of the state of the art regarding modular geometric properties in variable exponent spaces.

Suggested Citation

  • Mohamed A. Khamsi & Osvaldo D. Méndez & Simeon Reich, 2022. "Modular Geometric Properties in Variable Exponent Spaces," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2509-:d:866180
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    References listed on IDEAS

    as
    1. M. Bachar & M. A. Khamsi & O. Mendez & M. Bounkhel, 2019. "A geometric property in ℓp(·) and its applications," Mathematische Nachrichten, Wiley Blackwell, vol. 292(9), pages 1931-1940, September.
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    Cited by:

    1. Mohamed A. Khamsi & Osvaldo D. Méndez, 2022. "Remark on a Fixed-Point Theorem in the Lebesgue Spaces of Variable Integrability L p (·)," Mathematics, MDPI, vol. 11(1), pages 1-6, December.

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