Convexity and generalized Bernstein polynomials
نویسندگان
چکیده
منابع مشابه
Multivariate Bernstein polynomials and convexity
It is well known that in two or more variables Bernstein polynomi-als do not preserve convexity. Here we introduce two variations, one stronger than the classical notion, the other one weaker, which are preserved. Moreover, a weaker suucient condition for the monotony of subsequent Bernstein polynomials is given. linearly independent, in the course of which d has to be greater than or equal to ...
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We begin by classifying all solutions of two natural recurrences that Bernstein polynomials satisfy. The first scheme gives a natural characterization of Stancu polynomials. In Section 2, we identify the Bernstein polynomials as coefficients in the generating function for the elementary symmetric functions, which gives a new proof of total positivity for Bernstein polynomials, by identifying th...
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This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true. 1999 Elsevier Science B.V. Al...
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One of the greatest pleasures in mathematics is the surprising connections that often appear between apparently disconnected ideas and theories. Some particularly striking instances exist in the interaction between probability theory and analysis. One of the simplest is the elegant proof of the Weierstrass approximation theorem by S. Bernstein [2]: on the surface, this states that if f : [0, 1]...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1999
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500020101