On φ-contractions and fixed point results in fuzzy metric spaces

In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.

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