New Modular Fixed-Point Theorem in the Variable Exponent Spaces ℓp(.)

Amnay El Amri; Mohamed A. Khamsi

doi:10.3390/math10060869

New Modular Fixed-Point Theorem in the Variable Exponent Spaces ℓ_p(.)

Amnay El Amri, Mohamed A. Khamsi

Mathematics

Hassan II University

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

Abstract

In this work, we prove a fixed-point theorem in the variable exponent spaces ℓ_p(.), when p⁻ = 1 without further conditions. This result is new and adds more information regarding the modular structure of these spaces. To be more precise, our result concerns ρ-nonexpansive mappings defined on convex subsets of ℓ_p(.) that satisfy a specific condition which we call “condition of uniform decrease”.

Original language	British English
Article number	869
Journal	Mathematics
Volume	10
Issue number	6
DOIs	https://doi.org/10.3390/math10060869
State	Published - 1 Mar 2022

Keywords

Electrorheological fluid
Fixed point
Modular vector space
Nakano
Strictly convex
Uniformly convex

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10.3390/math10060869

Cite this

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title = "New Modular Fixed-Point Theorem in the Variable Exponent Spaces ℓp(.)",

abstract = "In this work, we prove a fixed-point theorem in the variable exponent spaces ℓp(.), when p− = 1 without further conditions. This result is new and adds more information regarding the modular structure of these spaces. To be more precise, our result concerns ρ-nonexpansive mappings defined on convex subsets of ℓp(.) that satisfy a specific condition which we call “condition of uniform decrease”.",

keywords = "Electrorheological fluid, Fixed point, Modular vector space, Nakano, Strictly convex, Uniformly convex",

author = "{El Amri}, Amnay and Khamsi, {Mohamed A.}",

note = "Funding Information: Funding: Khalifa University research project No. 8474000357. Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

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N2 - In this work, we prove a fixed-point theorem in the variable exponent spaces ℓp(.), when p− = 1 without further conditions. This result is new and adds more information regarding the modular structure of these spaces. To be more precise, our result concerns ρ-nonexpansive mappings defined on convex subsets of ℓp(.) that satisfy a specific condition which we call “condition of uniform decrease”.

AB - In this work, we prove a fixed-point theorem in the variable exponent spaces ℓp(.), when p− = 1 without further conditions. This result is new and adds more information regarding the modular structure of these spaces. To be more precise, our result concerns ρ-nonexpansive mappings defined on convex subsets of ℓp(.) that satisfy a specific condition which we call “condition of uniform decrease”.

KW - Electrorheological fluid

KW - Fixed point

KW - Modular vector space

KW - Nakano

KW - Strictly convex

KW - Uniformly convex

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New Modular Fixed-Point Theorem in the Variable Exponent Spaces ℓ_p(.)

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Keywords

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