Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points

Our manuscript puts forward two novel fuzzy proximal contractive conditions. First, we present two variants of fuzzy α-proximal quasi-H-contractions and establish optimal coincidence point outcomes for these contractions in fuzzy metric space. This manuscript’s second part proposes the fuzzy ψ-contraction for a multivalued mapping equipped with fuzzy weak P-property and achieves the best proximity point outcome in strong fuzzy metric space. The findings of this study broaden and generalize some existing research results.