Exploring Fixed-Point Theorems in <i>k</i>-Fuzzy Metric Spaces: A Comprehensive Study

Abstract

Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters (t1,t2,t3,⋯,tk) 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.

Keywords

• k-fuzzy metric space
• fixed point
• fuzzy contraction