Advancements in Fixed Point Theory for Fuzzy Normed Spaces Using the Common Limit Range Method with Application

This paper explores novel fixed point theorems for weakly compatible mappings in fuzzy normed spaces that adhere to an implicit relation. By employing the concepts of the common limit range property and the common property we establish new results in this field. Several illustrative examples are provided to validate the hypotheses and highlight the applicability of our findings. Furthermore, as an applied approach of our primary results, we establish a common fixed point theorem of integral type within fuzzy normed space.