Wijsman and Wijsman Randomly Triple Ideal Convergence Sequences of Sets in Probabilistic Metric Spaces

Many authors have extended the concept of convergence from number sequences to sequences of sets. In this paper, we focus on two notable adaptations: Wijsman convergence and randomly ideal convergence. We introduce and analyze several new types of convergence for sequences of sets: IψW3-convergence, I∗,ψW3-convergence, IψW3-Cauchy, I∗,ψW3-Cauchy, (IψW3, IψW)-convergence, and (I∗,ψW3, I∗,ψ)-convergence. These new concepts expand the framework of convergence and provide a deeper understanding of the behavior of set sequences under various conditions. Through rigorous analysis, we demonstrate the relationships between these new forms of convergence and their classical counterparts, highlighting their theoretical significance and potential applications in mathematical analysis and related fields. Our findings offer a comprehensive exploration of these advanced convergence concepts, paving the way for further research and development in this area.