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On Bernstein approximation problem

✍ Scribed by P.K Geetha

Publisher
Elsevier Science
Year
1969
Tongue
English
Weight
694 KB
Volume
25
Category
Article
ISSN
0022-247X

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πŸ“œ SIMILAR VOLUMES

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A partial solution to the affine Bernstein problem is given. The elliptic paraboloid is characterized as a locally strongly convex, affine complete, affine-maximal surface in A 3, satisfying a certain growth condition, about its afline Gauss-Kronecker curvature.

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✍ T.F. Xie; S.P. Zhou πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 161 KB

By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic