Modular Geometric Properties in Variable Exponent Spaces

Mohamed A. Khamsi; Osvaldo D. Méndez; Simeon Reich

doi:10.3390/math10142509

Modular Geometric Properties in Variable Exponent Spaces

Mohamed A. Khamsi
, Osvaldo D. Méndez
, Simeon Reich

Mathematics

University of Texas at El Paso
Technion–Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	British English
Article number	2509
Journal	Mathematics
Volume	10
Issue number	14
DOIs	https://doi.org/10.3390/math10142509
State	Published - Jul 2022

Keywords

electrorheological fluid
fixed point
modular vector space
Nakano modular
strictly convex
uniformly convex modular

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10.3390/math10142509

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title = "Modular Geometric Properties in Variable Exponent Spaces",

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.",

keywords = "electrorheological fluid, fixed point, modular vector space, Nakano modular, strictly convex, uniformly convex modular",

author = "Khamsi, \{Mohamed A.\} and M{\'e}ndez, \{Osvaldo D.\} and Simeon Reich",

note = "Funding Information: Mohamed A. Khamsi was funded by Khalifa University, UAE, under grant No. 8474000357. The author, therefore, gratefully acknowledges with thanks Khalifa University{\textquoteright}s technical and financial support. Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. All the authors are grateful to the editors and the referees for their useful comments and suggestions. Publisher Copyright: {\textcopyright} 2022 by the authors.",

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doi = "10.3390/math10142509",

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AU - Méndez, Osvaldo D.

AU - Reich, Simeon

N1 - Funding Information: Mohamed A. Khamsi was funded by Khalifa University, UAE, under grant No. 8474000357. The author, therefore, gratefully acknowledges with thanks Khalifa University’s technical and financial support. Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. All the authors are grateful to the editors and the referees for their useful comments and suggestions. Publisher Copyright: © 2022 by the authors.

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N2 - 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.

AB - 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.

KW - electrorheological fluid

KW - fixed point

KW - modular vector space

KW - Nakano modular

KW - strictly convex

KW - uniformly convex modular

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DO - 10.3390/math10142509

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SN - 2227-7390

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ER -

Modular Geometric Properties in Variable Exponent Spaces

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