Bivariate right fractional polynomial monotone approximation
Abstract
Let f ∈ Cr,p ([O, 1]2), r, p ∈ ℕ, and let L be a linear right fractional mixed partial differential operator such that L (f) ≥ 0, for all (x, y) in a critical region of [0, 1]2 that depends on L. Then there exists a sequence of two-dimensional polynomials Qm1,m2 (x, y) with L (Qm1,m2 (x, y)) ≥ 0 there, where m1, m2 ∈ ℕ such that m1 > r, m2 > p, so that f is approximated right fractionally simultaneously and uniformly by Qm1,m2 on [0, 1]2. This restricted right fractional approximation is accomplished quantitatively by the use of a suitable integer partial derivatives two-dimensional first modulus of continuity.
Publication Title
Springer Proceedings in Mathematics and Statistics
Recommended Citation
Anastassiou, G. (2016). Bivariate right fractional polynomial monotone approximation. Springer Proceedings in Mathematics and Statistics, 155, 19-31. https://doi.org/10.1007/978-3-319-28443-9_2
