Abstract
The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper, in the setting of modular metric spaces, we introduce the class of (JS)-omega-contractions and establish certain fixed point results. As application of our results, we deduce some Suzuki type theorems in modular metric space. Moreover, we introduce some notions of continuity in the setting of fuzzy metric spaces and obtain some results of fixed point for self-mappings defined on a fuzzy metric space as consequence of those given for modular metric space. An example is furnished to demonstrate the validity of the obtained results.