Open AccessA certain class of deferred weighted statistical B-summability involving (p,q)-integers and analogous approximation theorems
Author(s) -
Amjed Zraiqat,
Susanta Kumar Paikray,
Hemen Dutta
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1905425z
Subject(s) - mathematics , sequence (biology) , class (philosophy) , banach space , type (biology) , order (exchange) , modulus of continuity , discrete mathematics , convergence (economics) , combinatorics , pure mathematics , ecology , genetics , finance , artificial intelligence , computer science , economics , biology , economic growth
The preliminary idea of statistical weighted B-summability was introduced by Kadak et al. [27]. Subsequently, deferred weighted statistical B-summability has recently been studied by Pradhan et al. [38]. In this paper, we study statistical versions of deferred weighted B-summability as well as deferred weighted B-convergence with respect to the difference sequence of order r (> 0) involving (p,q)-integers and accordingly established an inclusion between them. Moreover, based upon our proposed methods, we prove an approximation theorem (Korovkin-type) for functions of two variables defined on a Banach space CB(D) and demonstrated that, our theorem effectively improves and generalizes most (if not all) of the existing results depending on the choice of (p,q)-integers. Finally, with the help of the modulus of continuity we estimate the rate of convergence for our proposed methods. Also, an illustrative example is provided here by generalized (p,q)-analogue of Bernstein operators of two variables to demonstrate that our theorem is stronger than its traditional and statistical versions.