New Modular Fixed-Point Theorem in the Variable Exponent Spaces <i>ℓ</i>_<i>p</i>(.)

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