On the Property of Monotonic Convergence for Beta Operators

Author: Adell J.A.   German Badia F.   de la Cal J.   Plo F.  

Publisher: Academic Press

ISSN: 0021-9045

Source: Journal of Approximation Theory, Vol.84, Iss.1, 1996-01, pp. : 61-73

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Abstract

We show that beta operators satisfy the property of monotonic convergence under convexity. This gives a positive answer to a question recently posed by M. K. Khan. Some additional properties, consequences and applications are also discussed. Throughout this paper, probabilistic methods play a fundamental role.