Exploring Fixed Point Theorems in Complex Valued Fuzzy Metric Spaces

Abstract

The scope of this note encompasses an extension of common fixed-point results from their initial establishment in complex-valued metric spaces to the realm of complex-valued fuzzy metric spaces. By adopting a nuanced approach, these outcomes are further demonstrated within the context of complex-valued fuzzy metric spaces, focusing on employing more lenient contractive criteria. Building upon the groundwork laid by previous researchers and considering a range of other relevant studies, our current research makes significant strides in enhancing and expanding upon their findings. While these prior works have primarily focused on complex-valued metric spaces, our study takes a significant leap forward by applying their insights to complex-valued fuzzy metric spaces. This extension of previous research deepens our understanding of these intricate spaces and opens up new avenues for exploring the complexities inherent in such settings. To enhance the clarity of our core findings, we offer illustrative examples that lend visual support to our assertions.