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The present paper concerns with the nonlinear Bernstein operators NBnf of the form

acting on bounded functions on an interval [0; 1] ; where Pn;k satisfy some suitable assumptions. As a continuation of the very recent paper of the authors [11], we estimate the rate of convergence by modulus of continuity and provide a Voronovskaya-type formula for these operators. We note that our results are strict extensions of the classical ones, namely, the results dealing with the linear Bernstein polynomials.

Mathematics Subject Classification (2010): 41A35, 41A25, 47G10.

Keywords: Nonlinear Bernstein operators, modulus of continuity, moments, Voronovskaya-type formula, (L-y ) Lipschitz condition, pointwise convergence.