Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces and application in stability of functional equation. (English) Zbl 1240.54025
Summary: In this paper, we define and study Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces. Further, we consider finite-dimensional Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces and prove some theorems about completeness, compactness and weak convergence in these spaces. As an application, we get a stability result in the setting of Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces.
MSC:
54A40 | Fuzzy topology |
54E50 | Complete metric spaces |
39B82 | Stability, separation, extension, and related topics for functional equations |