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Zbl 1012.41016
Abel, Ulrich; Ivan, Mircea
A Kantorovich variant of the Bleimann, Butzer and Hahn operators. (English)
[A] Proceedings of the fourth international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 22-28, 2000. Vol. I. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 68(1), 205-218 (2002).

The authors introduce a Kantorovich variant of the Bleimann, Butzer and Hahn operators as an approximation process for locally integrable functions defined by $$K_n(f;x)= {n+2\over(1+x)^n} \sum^n_{k=0}{n \choose k}x^k \int^{k+1 \over n+1-k}_{k \over n+2-k} {f(t)\over (1+t)^2}dt.$$ They prove, among others, that $K_n(f,x)$ converge pointwise at each continuity point of a wide class of locally integrable functions, deal also with the rate of convergence, and the asymptotic behaviour.
[Laszlo Leindler (Szeged)]

MSC 2000:: *41A25 Degree of approximation, etc.

Keywords: Bleimann operators; Hahn operators

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