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

In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in Lp(·)(Ω) obtained under the assumptions p+<∞ and the property (R) satisfied by ρ will force p−>1. Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption p+<∞.