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

Amnay El Amri and Mohamed A. Khamsi
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Amnay El Amri: Faculté des Sciences Ben Msik (LAMS), Hassan II University, Casablanca 21100, Morocco
Mohamed A. Khamsi: Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi 127788, United Arab Emirates

Mathematics, 2022, vol. 10, issue 6, 1-13

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”.

Keywords: electrorheological fluid; fixed point; modular vector space; Nakano; strictly convex; uniformly convex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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