A Note on the Kadec-Klee Property
Abstract
The objective of this paper is to rigorously define the Kadec-Klee property for modular spaces endowed with a sequential convergence structure, and to demonstrate that this property leads to normal structure in such spaces. Consequently, we establish that the Kadec-Klee property defined herein implies the corresponding fixed point property for these spaces. These results are new in the modular space setting. Furthermore, given that the examined class of spaces encompasses Banach spaces, modular function spaces, and various other types of spaces, our theory offers a comprehensive, unified framework for exploring the interconnections between the Kadec-Klee property, normal structure, and the fixed point property.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Advanced Topology and Set Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Axioms
- Publisher
- MDPI AG
- Volume
- 15
- Issue
- 2
- Pages
- 115–115
- Publication date
- 4 February 2026
- Language
- EN