Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces

Abstract

The current manuscript aims to introduce complex-valued intuitionisitic fuzzy metric spaces as a fresh perspective on complex-valued fuzzy metric spaces and intuitionistic fuzzy metric spaces. Existence together with distinctiveness of the fixed points within maps with diverse contractive criteria in this novel space are established. Additionally, our work yields a few common fixed-point findings for intuitionistic fuzzy Banach contraction on this newly introduced space. The outcomes presented in this study go beyond the existing literature, adding to the growing body of knowledge in this field. Our research outcomes are exemplified through examples that are included in this paper to help readers better grasp our findings. Our paper concludes with a discussion of how our findings can be applied to the problem of determining the presence of an exclusive solution for Fredholm integral equations.