Characterization of deferred type statistical convergence and P‐summability method for operators: Applications to q‐Lagrange–Hermite operator. (7th October 2022)

• Record Type: Journal Article
• Authors: Agrawal, Purshottam Narain; Shukla, Rahul; Baxhaku, Behar
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 4449
• Page End: 4465
• Publication Date: 2022-10-07
• Subjects: deferred type statistical convergence -- modulus of continuity -- multivariate Lagrange–Hermite polynomials -- P$$ P $$‐summability -- q$$ q $$‐Lagrange–Hermite polynomials; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8770
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.