Exploring Fixed-Point Theorems in k-Fuzzy Metric Spaces: A Comprehensive Study

Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters (t[sub.1] ,t[sub.2] ,t[sub.3] ,⋯,t[sub.k] ) and the authors presented an analogue of Grabiec’s fixed-point result in k -fuzzy metric spaces along with other necessary notions. The results presented only addressed continuous mappings. For discontinuous mappings, there is no result in k -fuzzy metric spaces. In this paper, we obtain some fixed-point results stating necessary conditions for the existence of fixed points of mappings eliminating the continuity requirement in k -fuzzy metric spaces. We illustrate the hypothesis of our findings with examples. We provide a common fixed-point theorem and fixed-point theorems for single-valued k-fuzzy Kannan type contractions. As an application, we use a fixed-point result to ensure the existence of solution of fractional differential equations.