This research presents new fixed-point theorems for weak probabilistic φ-contractions in Menger probabilistic metric spaces, highlighting novel concepts like ZH-sets.
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.
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Zheng et al. (2025) studied this question.
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