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Bernstein type operators having 1 and x j as fixed points

Zoltán Finta — 2013

Open Mathematics

For certain generalized Bernstein operators {L n} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i(x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points.

Approximation by q -Bernstein type operators

Zoltán Finta — 2011

Czechoslovak Mathematical Journal

Using the q -Bernstein basis, we construct a new sequence { L n } of positive linear operators in C [ 0 , 1 ] . We study its approximation properties and the rate of convergence in terms of modulus of continuity.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

Finta, Zoltán — 2004

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36. We establish direct and converse theorems for generalized parameter dependent Bernstein-type operators. The direct estimate is given using a K-functional and the inverse result is a strong converse inequality of type A, in the terminology of [2].

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