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Limiting properties of Inverse Beta and generalized Bleimann–Butzer–Hahn operators

Published online by Cambridge University Press:  24 October 2008

José A. Adell  and
Jesús De La Cal
José A. Adell
Affiliation:
Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Jesús De La Cal
Affiliation:
Departamento de Matemática Aplicada y Estadística e Investigación Operativa, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
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Abstract

In this paper, we consider limiting properties concerning linear operators of probabilistic type. Specifically, we show that gamma operators are limits of inverse Beta operators and that Bleimann–Butzer–Hahn, Szász and Baskakov operators are limits of generalized Bleimann–Butzer–Hahn operators. By duality, these results are closely related to the convergence in the total variation distance of the probability measures involved. In each case, rates of convergence are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 489 - 498
Copyright
Copyright © Cambridge Philosophical Society 1993

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