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.


40A35 Ideal and statistical convergence
41A36 Approximation by positive operators


Zbl 0953.40002
Full Text: DOI


[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) · Zbl 1513.40062
[8] Altomare, F.; Ampiti, M., (Korovkin-type Approximation Theory and its Applications. Korovkin-type Approximation Theory and its Applications, de Gruyter Stud. Math., vol. 17 (1994), Walter de Gruyter: Walter de Gruyter Berlin) · Zbl 0924.41001
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.