An application of almost convergence in approximation theorems. (English) Zbl 1252.41022
Summary: The concept of almost convergence was introduced by G. G. Lorentz [Acta Math., Uppsala 80, 167–190 (1948; Zbl 0031.29501)] has various applications. In this work, we apply this method to prove some Korovkin-type approximation theorems.
MSC:
| 41A36 | Approximation by positive operators |
Citations:
Zbl 0031.29501References:
| [1] | S. Banach, Théorie des Operations Lineaires, Warsaw, 1932.; S. Banach, Théorie des Operations Lineaires, Warsaw, 1932. · JFM 58.0420.01 |
| [2] | Lorentz, G. G., A contribution to theory of divergent sequences, Acta Math., 80, 167-190 (1948) · Zbl 0031.29501 |
| [3] | Gadz˘iev, A. D., The convergence problems for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P.P. Korovkin, Soviet Math. Dokl., 15, 1433-1436 (1974) · Zbl 0312.41013 |
| [4] | Dirik, F.; Demirci, K., Korovkin type approximation theorem for functions of two variables in statistical sense, Turk. J. Math., 33, 1-11 (2009) |
| [5] | Edely, O. H.H.; Mohiuddine, S. A.; Noman, A. K., Korovkin type approximation theorems obtained through generalized statistical convergence, Appl. Math. Lett., 23, 11, 1382-1387 (2010) · Zbl 1206.40003 |
| [6] | Ahmad, Z. U.; Mursaleen, An Application of Banach limits, Proc. Amer. Math. Soc., 103, 1, 244-246 (1988) · Zbl 0652.40009 |
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