Partial shape preserving approximation by bivariate Hermite-Fejér polynomials
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-Fejér 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. © 2001 Elsevier Science Ltd.
Computers and Mathematics with Applications
Anastassiou, G., & Gal, S. (2001). Partial shape preserving approximation by bivariate Hermite-Fejér polynomials. Computers and Mathematics with Applications, 42 (1-2), 57-64. https://doi.org/10.1016/S0898-1221(01)00130-4