Intimate Mappings in Interval-Valued Fuzzy Metric Space: A Few Fixed-Point Findings - Naval Singh; Umashankar Singh; Ruchi Singh (Recent Trends in Mathematics, 2024)
The purpose of this study is to extend some previously established fixed point results for interval valued fuzzy metric space. For this objective, various contractive criteria with respect to an intimate mapping are applied. We employ intimate mapping in interval valued fuzzy metric space (IVFMS) to validate some well-known fixed point results. Our findings complement and generalize the recent findings of the common fixed point theorem for intimate mapping. The primary aim of this study is to build upon and extend the existing fixed point results within the realm of interval-valued fuzzy metric spaces (IVFMS). Fixed point theorems are crucial in various mathematical and applied fields, providing solutions to equations where a function maps a point to itself. In this research, we focus on applying diverse contractive conditions specifically in the context of intimate mappings to achieve our objectives. Intimate mapping, a relatively novel concept in IVFMS, plays a key role in our analysis. By employing this type of mapping, we are able to verify and validate several well-established fixed point results within IVFMS. This approach not only supports the known results but also broadens their applicability, thereby enhancing the theoretical foundation of fixed point theorems in fuzzy metric spaces. Our findings make significant contributions by complementing and generalizing recent discoveries related to the common fixed point theorem for intimate mappings. In essence, this study provides a deeper and more comprehensive understanding of fixed point theorems, showcasing the versatility and robustness of intimate mappings in interval-valued fuzzy metric spaces. This advancement opens new avenues for future research and potential applications in various scientific and engineering disciplines where fuzzy metric spaces are utilized.
Keywords: Common fixed point; Fixed Point; Interval-valued fuzzy metric; Intimate mappings. Contractive condition