Probabilistic contraction under a control function (Q2022310)

In this paper, the authors have established some fixed point theorems in probabilistic metric spaces. A new contraction mapping defined in such spaces has been shown to have a unique fixed point if such spaces are \(G\)-complete with an arbitrary choice of a continuous \(t\)-norm. The contraction defined with the help of a control function is different from those of several authors used in probabilistic fixed point theory. The methodology employed by the authors of the present article in the proof is new and an illustrative example is also given.