Statistical Soft Wijsman Convergence

The concept of convergence is a fundamental tool for building or understanding a mathematical structure. In particular, many applied areas of mathematics require the analysis of sets or set-based approximations. A notable example is Wijsman convergence, a type of set convergence defined as the distance from a point to a set as determined by a metric function. Another important concept in our study is soft set theory, which generalizes classical set theory and provides an effective approach to addressing uncertainties in a parametric manner. Building on this foundation, we introduce the concepts of statistical and lacunary statistical convergence in the sense of Wijsman for sequences of closed sets within the framework of soft metric spaces. We establish fundamental properties associated with these types of convergence and explore their interrelationships, resulting in several inclusion results. Furthermore, we utilize a generalized version of the natural density function, referred to as the ϕ-weighted density function, to strengthen our findings.