Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind
Joint Authors
Coroianu, Lucian
Gal, Sorin G.
Bede, Barnabás
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-09
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
Starting from the study of the Shepard nonlinear operator of max-prod type by Bede et al.
(2006, 2008), in the book by Gal (2008), Open Problem 5.5.4, pages 324–326, the Bernstein max-prod-type operator is introduced and the question of the approximation order by this operator is raised.
In recent paper, Bede and Gal by using a very complicated method to this open question an answer is given by obtaining an upper estimate of the approximation error of the form Cω1(f;1/n) (with an unexplicit absolute constant C>0) and the question of improving the order of approximation ω1(f;1/n) is raised.
The first aim of this note is to obtain this order of approximation but by a simpler method, which in addition presents, at least, two advantages: it produces an explicit constant in front of ω1(f;1/n) and it can easily be extended to other max-prod operators of Bernstein type.
However, for subclasses of functions f including, for example, that of concave functions, we find the order of approximation ω1(f;1/n), which for many functions f is essentially better than the order of approximation obtained by the linear Bernstein operators.
Finally, some shape-preserving properties are obtained.
American Psychological Association (APA)
Bede, Barnabás& Coroianu, Lucian& Gal, Sorin G.. 2009. Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-26.
https://search.emarefa.net/detail/BIM-483252
Modern Language Association (MLA)
Bede, Barnabás…[et al.]. Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-26.
https://search.emarefa.net/detail/BIM-483252
American Medical Association (AMA)
Bede, Barnabás& Coroianu, Lucian& Gal, Sorin G.. Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-26.
https://search.emarefa.net/detail/BIM-483252
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483252