On convergence of certain nonlinear Bernstein operators

Harun KARSLI, Ismail Ugur TIRYAKI, Huseyin Erhan ALTIN


The present paper concerns with the very recently introduced nonlinear Bernstein operators NB_{n}f of the form


acting on bounded functions on an interval [0,1], where P_{n,k} satisfy some suitable assumptions. As a continuation of the very recent paper of the authors <cite>kta</cite>, we estimate their pointwise convergence to a function f having derivatives of bounded (Jordan) variation on the interval [0,1].
We note that our results are strict extensions of the classical ones, namely, the results dealing with the linear Bernstein polynomials.

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