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STUDIA MATHEMATICA - Issue no. 2 / 2015 | |||||||
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A VORONOVSKAYA-TYPE THEOREM FOR A CERTAIN NONLINEAR BERNSTEIN OPERATORS. Authors: . |
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Abstract: 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. |
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