The summation methods were combined under a single heading which is called Summability Methods and have been used efficiently in classical and modern mathematics. With the rapid development of sequence spaces, the concept of statistical convergence, which was independently introduced by Fast Fast and Steinhaus Steinhaus in the year 1951, attracts great attention of researchers. In 1900, Pringsheim Pringsheim introduced the notion of convergence for double sequences. The chapter is devoted to extend the notions of weighted statistical summability and weighted statistical convergence which are largely used to obtain interesting applications to approximation theorems. Due to the rapid development of quantum calculus, many authors have focused on the concept of post-quantum calculus which has been used efficiently in many fields of science, in particular, approximation theory, differential equations, Lie groups, field theory, probability, oscillator algebra, hypergeometric series, and physical sciences. The foundation of the theory of approximation by positive linear operators was introduced independently by Bohman Bohman and Korovkin Korovkin.