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Generalized equi-statistical convergence of positive linear operators and associated approximation theorems
- Source :
-
Mathematical & Computer Modelling . May2012, Vol. 55 Issue 9/10, p2040-2051. 12p. - Publication Year :
- 2012
-
Abstract
- Abstract: The concepts of equi-statistical convergence, statistical pointwise convergence and statistical uniform convergence for sequences of functions were introduced recently by Balcerzak et al. [M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007) 715–729]. In this paper, we use the notion of -statistical convergence in order to generalize these concepts. We establish some inclusion relations between them. We apply our new notion of -equi-statistical convergence to prove a Korovkin type approximation theorem and we show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally, we prove a Voronovskaja type approximation theorem via the concept of -equi-statistical convergence. Some interesting examples are also displayed here in support of our definitions and results. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 08957177
- Volume :
- 55
- Issue :
- 9/10
- Database :
- Academic Search Index
- Journal :
- Mathematical & Computer Modelling
- Publication Type :
- Academic Journal
- Accession number :
- 73766762
- Full Text :
- https://doi.org/10.1016/j.mcm.2011.12.011