Probabilistic Generalized Metric Spaces and Nonlinear Contractions

Abstract

We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

Keywords

• probabilistic (fuzzy) generalized metric spaces
• fixed points
• nonlinear contractions