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V. Totik (1994)
APPROXIMATION BY BERNSTEIN POLYNOMIALSAmerican Journal of Mathematics, 116
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to The Forum D’Analystes 2022
- ISSN
- 0971-3611
- eISSN
- 2367-2501
- DOI
- 10.1007/s41478-022-00430-0
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain [inline-graphic not available: see fulltext], has been introduced and several results, similar to well-known results of bivariate constrained approximation in terms of dimension preserving approximants, have been established. Further, some clue for the construction of bivariate dimension preserving approximants, using the concept of fractal interpolation functions, has been added. In the last part, some multi-valued fractal operators associated with bivariate α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha $$\end{document}-fractal functions are defined and studied.
Journal
The Journal of Analysis – Springer Journals
Published: Dec 1, 2022
Keywords: Fractal dimension; Fractal interpolation; Fractal surfaces; Bernstein polynomials; Bivariate constrained approximation; Primary 28A80; Secondary 10K50; 41A10