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Partial shape preserving approximation by bivariate Hermite-Fejér polynomials

✍ Scribed by G.A. Anastassiou; S.G. Gal

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
354 KB
Volume
42
Category
Article
ISSN
0898-1221

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✦ Synopsis

Extending the results from the univariate case in a paper by Gal and Szabados, in this paper, we prove that the bivariate interpolation operators of Hermite-Fej@r preserve some kinds of monotonicity and convexity of bivariate functions, in the neighborhoods of some points. Also, quantitative results are proved, i.e., estimates of the magnitudes for these neighborhoods are obtained.

📜 SIMILAR VOLUMES

Saturation Problem ofLp-Approximation by
Saturation Problem ofLp-Approximation by Hermite–Fejér Interpolation
✍ G. Min 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 342 KB

The saturation of L p -approximation of Hermite Feje r interpolation based on the zeros of generalized Jacobi polynomials is considered. Although mean convergence may improve the approximation order compared to uniform convergence, surprisingly, their saturation orders are exactly same, that is, 1Ân