Fixed Point Theorems in Fuzzy Metric Spaces via Generalized Rational-Type Contractions.

In this paper, we create new fixed point (FP) theorems for self-mappings in fuzzy metric spaces (FMS). Utilizing properties of fuzzy metrics (FM) and continuous t-norms, we derive sufficient conditions under which a mapping admits a unique FP, and we prove that the sequence of iterates converges to this point. The results presented extend and generalize existing theorems by incorporating nonlinear contractive conditions involving fuzzy distances. An example is provided to illustrate the applicability of the main results. A graphical representation of the FM is also discussed.