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q-parametric Bleimann Butzer and Hahn operators. (English) Zbl 1154.41012

Let the q-Bernstein polynomials are given by

B n,q (f)(x):= k=0 n f[k] [n]n kx k s=0 n-k-1 (1-q s x)·

In this paper, a q-analog of the Bleimann, Butzer and Hahn operators of the form

H n,q (f)(x):=(Φ -1 B n+1,q Φ)(f)(x)

is proposed, where Φ:C p * [0,)C[0,1] is a suitable positive linear isomorphism. The authors study the properties of the q-BBH operators H n,q and establish the rate of convergence. A Voronovskaja-type theorem and saturation of convergence for q-BBH operators for 0<q<1 is discussed. Further, the convergence of the derivative of q-BBH operators is considered.

41A36Approximation by positive operators
41A40Saturation (approximations and expansions)
41A25Rate of convergence, degree of approximation