Characterization of deferred type statistical convergence and P‐summability method for operators: Applications to q‐Lagrange–Hermite operator

摘要

The present work considers two important convergence techniques, namely, deferred type statistical convergence and P$$ P $$‐summability method in respect of linear positive operators. With regard to these techniques, following closely the ideas developed in the articles (Appl. Math. Lett. 18, 2005, 1339‐1344, and Sau Paulo J. Math. Sci. 13, 2019, 696‐707), we state and prove two general non‐trivial Korovkin‐type approximation results for positive linear operators. Further, we define an operator based on multivariate q$$ q $$‐Lagrange–Hermite polynomials and exhibit the applicability of the above theorems to these operators.