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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 [{\it 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.

40A35Ideal and statistical convergence
41A36Approximation by positive operators
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
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[10] P.P. Korovkin, Linear operators and the theory of approximation, India, Delhi, 1960. · Zbl 0107.05302