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Note on a Korovkin-type theorem

Authors:	Zoltá n Finta

Affiliation:	Babe?-Bolyai University, Department of Mathematics, 1, M. Kog?lniceanu st., 400084 Cluj-Napoca, Romania

Abstract:	A new Korovkin-type theorem and its converse theorem are established. We compare our direct result with the Korovkin-type theorem given by Wang [15]. As applications we obtain quantitative estimates for q -Bernstein-type operators which preserve the functions _e₀(x)=1 $e_{0} (x) = 1$ and _e_j(x)=x^j $e_{j} (x) = x^{j}$ .

Keywords:	Korovkin-type theorem First order Ditzian&ndash Totik modulus of smoothness q-Bernstein-type operators
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