A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems

Authors

L. N. Mishra, Vellore Institute of Technology (VIT) University
M. Patro, Veer Surendra Sai University of Technology
S. K. Paikray, Veer Surendra Sai University of Technology
B. B. Jena, Veer Surendra Sai University of Technology

Abstract

Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a Banach space C_B(D). Finally, several illustrative examples are presented in light of our definitions and outcomes established in this paper.

Recommended Citation

Mishra, L. N.; Patro, M.; Paikray, S. K.; and Jena, B. B. (2019). A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems, Applications and Applied Mathematics: An International Journal (AAM), Vol. 14, Iss. 2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss2/6