Abstract
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+<∞.
Funder
Khalifa University
Israel Science Foundation
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference10 articles.
1. A fixed-point theorem for mappings which do not increase distances;Kirk;Am. Math. Mon.,1965
2. Khamsi, M.A., Méndez, O., and Reich, S. (2022). Modular geometric properties in variable exponent spaces. Mathematics, 10.
3. On geometric properties of the spaces lp(x);Pick;Rev. Mat. Complut.,2011
4. On spaces lp(x),wk,p(x);Czechoslov. Math. J.,1991
5. Diening, L., Harjulehto, P., Hästö, P., and Růžička, M. (2011). Lebesgue and Sobolev Spaces with Variable Exponents, Springer. Lecture Notes in Mathematics.