Remark on a Fixed-Point Theorem in the Lebesgue Spaces of Variable Integrability Lp(·)

Mohamed A. Khamsi; Osvaldo D. Méndez

doi:10.3390/math11010157

Remark on a Fixed-Point Theorem in the Lebesgue Spaces of Variable Integrability L^p(·)

Mohamed A. Khamsi
, Osvaldo D. Méndez

Mathematics

University of Texas at El Paso

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

Abstract

In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in (Formula presented.) obtained under the assumptions (Formula presented.) and the property (Formula presented.) satisfied by (Formula presented.) will force (Formula presented.). Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption (Formula presented.).

Original language	British English
Article number	157
Journal	Mathematics
Volume	11
Issue number	1
DOIs	https://doi.org/10.3390/math11010157
State	Published - Jan 2023

Keywords

electrorheological fluid
fixed point
modular strict convexity
modular uniform convexity
modular vector space
Nakano modular

Access to Document

10.3390/math11010157

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Cite this

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title = "Remark on a Fixed-Point Theorem in the Lebesgue Spaces of Variable Integrability Lp(·)",

abstract = "In a personal communication, Prof. Dom{\'i}nguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in (Formula presented.) obtained under the assumptions (Formula presented.) and the property (Formula presented.) satisfied by (Formula presented.) will force (Formula presented.). Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption (Formula presented.).",

keywords = "electrorheological fluid, fixed point, modular strict convexity, modular uniform convexity, modular vector space, Nakano modular",

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

note = "Funding Information: Khalifa University Research Project No. 8474000357 and Israel Science Foundation (Grant 820/17). 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. The second author acknowledges the support received while visiting Khalifa University. The authors thank Dom{\'i}nguez Benavides for his insight regarding the point developed in this note. Publisher Copyright: {\textcopyright} 2022 by the authors.",

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KW - modular strict convexity

KW - modular uniform convexity

KW - modular vector space

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