Bivariate left fractional pseudo-polynomial monotone approximation
In this article we deal with the following general two-dimensional problem: Let f be a two variable continuously differentiable real-valued function of a given order, let L* be a linear left fractional mixed partial differential operator and suppose that L* (f) ≥ 0 on a critical region. Then for sufficiently large n, m ∈ N, we can find a sequence of pseudo-polynomials Q*n,m in two variables with the property L* (Q*n,m) ≥ 0 on this critical region such that f is approximated with rates fractionally and simultaneously by Q*n,m in the uniform norm on the whole domain of f. This restricted approximation is given via inequalities involving the mixed modulus of smoothness ωs,q, s, q ∈ N, of highest order integer partial derivative of f.
Springer Proceedings in Mathematics and Statistics
Anastassiou, G. (2016). Bivariate left fractional pseudo-polynomial monotone approximation. Springer Proceedings in Mathematics and Statistics, 155, 1-17. https://doi.org/10.1007/978-3-319-28443-9_1