𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the image of the limit q-Bernstein operator

✍ Scribed by Sofiya Ostrovska

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
76 KB
Volume
32
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The limit q‐Bernstein operator B~q~ emerges naturally as an analogue to the Szász–Mirakyan operator related to the Euler distribution. Alternatively, B~q~ 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 B~q~ is a positive shape‐preserving linear operator on C[0, 1] with ∥B~q~∥=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 B~q~ are presented. Copyright © 2009 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

On the Iterates of Some Bernstein-Type O
On the Iterates of Some Bernstein-Type Operators
✍ José A Adell; F Germán Badı́a; Jesús de la Cal 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 184 KB

In this paper, we establish two basic functional-type identities between the iterates of the Bleimann᎐Butzer᎐Hahn operator and those of the Bernstein Ž . operator, on the one hand, and the iterates of the modified Meyer᎐Konig and Zeller operator and those of the Baskakov operator, on the other. Thes