Bivariate right 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 (Formula presented.) be a linear right fractional mixed partial differential operator and suppose that (Formula presented.) on a critical region. Then for sufficiently large n,m ∈ ℕ, we can find a sequence of pseudo-polynomials Q∗n,min two variables with the property (Formula presented.) on this critical region such that f is approximated with rates right 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.
Advances in Intelligent Systems and Computing
Anastassiou, G. (2016). Bivariate right fractional pseudo-polynomial monotone approximation. Advances in Intelligent Systems and Computing, 441, 15-31. https://doi.org/10.1007/978-3-319-30322-2_2