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.