Abstract
AbstractThe limit q‐Bernstein operator Bq emerges naturally as an analogue to the Szász–Mirakyan operator related to the Euler distribution. Alternatively, Bq comes out as a limit for a sequence of q‐Bernstein polynomials in the case 0<q<1. Lately, different properties of the limit q‐Bernstein operator and its iterates have been studied by a number of authors. In particular, it has been shown that Bq is a positive shape‐preserving linear operator on C[0, 1] with ∥Bq∥=1, which possesses the following remarkable property: in general, it improves the analytic properties of a function. In this paper, new results on the properties of the image of Bq are presented. Copyright © 2009 John Wiley & Sons, Ltd.
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