On Weak Probabilistic φ-Contractions in Menger Probabilistic Metric Spaces

Two new concepts are introduced in this paper: ZH-set and weak probabilistic φ-contraction. Firstly, a fixed-point theorem for weak probabilistic φ-contraction is given in Menger probabilistic metric spaces, which generalizes and unifies several results in the existing literature. Then, a best proximity point theorem is obtained. Finally, two examples are provided to prove the effectiveness of our results.