Statistical Convergence Restricted by Weight Functions and its Application in the Variation of γ-covers

In this paper, we utilize a weight function g to regulate the pace of the statistical convergence in a topological space. We extend the notion of statistical convergence to weighted statistical convergence by utilizing the weighted density. Using this intriguing idea of convergence, a new variation of γ-covers (referred to as s_g-γ cover) is introduced. Subsequently some topological analysis are conducted on the class of s_g-γ coverings. It is demonstrated that the new class of s_g-γ coverings lies some where between the class of γ-covers and the class of s-γ cover classes.