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Statistical summability and approximation by de la Vallée-Poussin mean. (English) Zbl 1216.40003

Appl. Math. Lett. 24, No. 3, 320-324 (2011); corrigendum ibid. 25, No. 3, 665 (2012).
The authors introduce two concepts of statistical \(\lambda\)-convergence and strongly \(\lambda _{q}\)-convergence \((0<q<\infty)\) and give some relations between \(\lambda\)-statistical convergence and these newly defined concepts. They also prove a Korovkin type approximation theorem by using the newly defined summability method.

MSC:

40A35 Ideal and statistical convergence
41A36 Approximation by positive operators
47A58 Linear operator approximation theory
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