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Korovkin type approximation theorems obtained through generalized statistical convergence. (English) Zbl 1206.40003
Authors’ abstract: The concept of \(\lambda\)-statistical convergence was introduced in [M. Mursaleen, Math. Slovaca, 50, No.1, 111–115 (2000; Zbl 0953.40002)] by using the generalized de la Vallée Poussin means. In this work we apply this method to prove some Korovkin type approximation theorems.

MSC:
40A35 Ideal and statistical convergence
41A36 Approximation by positive operators
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[1] Fast, H., Sur la convergence statistique, Colloq. math., 2, 241-244, (1951) · Zbl 0044.33605
[2] Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. math., 2, 73-74, (1951)
[3] Mursaleen, M., \(\lambda\)-statistical convergence, Math. slovaca, 50, 111-115, (2000) · Zbl 0953.40002
[4] Leindler, L., Über die de la vallée poussinsche summierbarkeit allgemeiner orthogonalreihen, Acta math. acad. sci. hung., 16, 375-387, (1965) · Zbl 0138.28802
[5] Gadz˘iev, A.D.; Orhan, C., Some approximation theorems via statistical convergence, Rocky mountain J. math., 32, 129-138, (2002) · Zbl 1039.41018
[6] Patterson, R.; Savas, E., Korovkin and weierstass approximation via lacunary statistical sequences, J. math. stat., 1, 2, 165-167, (2005) · Zbl 1142.41304
[7] Alotaibi, A., Some approximation theorems via statistical summability \((C, 1)\), Aligarh bull. math., 26, 2, 77-81, (2007)
[8] Altomare, F.; Ampiti, M., ()
[9] 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
[10] P.P. Korovkin, Linear operators and the theory of approximation, India, Delhi, 1960. · Zbl 0107.05302
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