Using the notion of fuzzy negation functions which naturally arises in the theory and applications of fuzzy logic, we enlarge the class of fuzzy ψ-contractions of (Formula presented.) type as well as the class of fuzzy (Formula presented.) contractions and generalize corresponding fixed point theorems. We show that strict negations, strong negations and Archimedean t-norms play a central role in the aforesaid fixed point theorems. Appropriate examples that illustrate the exposed theory are provided. In the process, we obtain a new type of topology (as well as convergence and completeness) for the fuzzy metric spaces that suggesting a potential new research avenue to explore the subject.
Martínez-Moreno et al. (Wed,) studied this question.