Displaying similar documents to “On the iterative combinations of Baskakov operator.”

Korovkin-type theorems and applications

Nazim Mahmudov (2009)

Open Mathematics

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Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.

Remarks on an article of J.P. King

Heiner Gonska, Paula Piţul (2005)

Commentationes Mathematicae Universitatis Carolinae

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The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.