Research
Statistical summability
(
C
,
1
)
and a Korovkin type approximation theorem
1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
2 Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
Journal of Inequalities and Applications 2012, 2012:172 doi:10.1186/1029-242X-2012-172
Published: 6 August 2012Abstract
The concept of statistical summability 
has recently been introduced by Móricz [Jour. Math. Anal. Appl. 275, 277-287 (2002)]. In this paper, we use this notion of summability to prove the Korovkin
type approximation theorem by using the test functions 1, 
, 
. We also give here the rate of statistical summability and apply the classical Baskakov operator to construct an example in support of our
main result.
MSC: 41A10, 41A25, 41A36, 40A30, 40G15.
Keywords:
statistical convergence; statistical summability; positive linear operator; Korovkin type approximation theorem
