Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind
نویسندگان
چکیده
منابع مشابه
Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind
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 o...
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Starting from the study of the Shepard nonlinear operator of maxprod type in [2], [3], in the recent monograph [4], Open Problem 5.5.4, pp. 324-326, the Baskakov max-prod type operator is introduced and the question of the approximation order by this operator is raised. The aim of this note is to obtain the order of uniform approximation Cω1(f ; 1 √ n ) (with the explicit constant C = 24) of an...
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In this paper firstly we extend from [0, 1] to an arbitrary compact interval [a, b], the definition of the nonlinear Bernstein operators of max-product kind, B n (f), n ∈ N, by proving that their order of uniform approximation to f is ω1(f, 1/ √ n) and that they preserve the quasi-concavity of f . Since B (M) n (f) generates in a simple way a fuzzy number of the same support [a, b] with f , it ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2009
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2009/590589