Weighted statistical convergence and its application to Korovkin type approximation theorem - Mursaleen, Mohammad; Karakaya, Vatan; Erturk, Muzeyyen; Gursoy, Faik (ELSEVIER SCIENCE INC, 2012)
The concept of weighted statistical convergence was introduced and studied by Karakaya and Chishti (2009) [7]. In this paper, we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability ((N) over bar, p(n)) due to Moricz and Orhan (2004) [10]. We apply this new summability method to prove a Korovkin type approximation theorem by using the test functions 1, e(-x), e(-2x). We apply the classical Baskakov operator to construct an example in support of our result. (C) 2012 Elsevier Inc. All rights reserved.
Keywords: Density; Statistical convergence; Weighted statistical convergence; Statistical summability ((N)over-bar, p(n)); Positive linear operator; Korovkin type approximation theorem; SUMMABILITY; Mathematics