A Voronovskaya-type theorem for a certain nonlinear Bernstein operators
A Voronovskaya-type theorem for a certain nonlinear Bernstein operators
The present paper concerns with the nonlinear Bernstein operators NBnf of the form (NB(n)f)(x) = Sigma(n)(k=0) P-n,P-k (x, f (k/n)), 0 <= x <= 1, n is an element of N, acting on bounded functions on an interval [0, 1], where P-n,P-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.
Moments, Modulus of Continuity, Voronovskaya-type Formula, Pointwise Convergence, (L-psi) Lipschitz Condition, Nonlinear Bernstein Operators
Moments, Modulus of Continuity, Voronovskaya-type Formula, Pointwise Convergence, (L-psi) Lipschitz Condition, Nonlinear Bernstein Operators
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