Fixed point results of contractions in modular metric spaces

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orliczs paces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings and modular contractive mappings in modular metric spaces.These are related to the successive approximations of fixed points (viaorbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.