Common Fixed Point Theorems for Multi-Fuzzy Mappings via Weak Contractive Conditions in MR-Metric Spaces

Author : A.N. Lakshmi Sudha, Dr. T. Rakesh Singh

Abstract : In this paper, we study common fixed point results for multiple fuzzy mappings in the framework of MR-metric spaces. By introducing a weaker weighted-sum contractive condition, we establish the existence and uniqueness of common fixed points for four and six fuzzy mappings in a complete MR-metric space. Using a cyclic iterative construction together with the Hausdorff MR-metric structure, we prove the convergence of the generated sequence and demonstrate that all the mappings admit a unique common f ixed point. The proposed results extend and strengthen existing fixed point principles by relaxing contraction assumptions and expanding the theory to multi-mapping settings. These findings further advance the development of fixed point theory in generalized metric spaces and provide a broader foundation for applications in fuzzy analysis, optimization, and uncertainty modeling.

Keywords : Fixed point, fuzzy mapping, MR-metric space, MR-metric, contraction principle.

Conference Name : National Conference on Applied Physics and Mathematics (NCAPM-26)

Conference Place : Visakhapatnam, India

Conference Date : 12th Apr 2026