Bivariate left fractional polynomial monotone approximation
Abstract
Let f ∈ Cr,p ([0, 1]2), r, p ∈ ℕ, and let L∗ be a linear left 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 (Formula presented.) with (Formula presented.) there, where (Formula presented.) such that (Formula presented.), so that f is approximated left fractionally simultaneously and uniformly by (Formula presented.) on [0, 1]2. This restricted left fractional approximation is accomplished quantitatively by the use of a suitable integer partial derivatives two-dimensional first modulus of continuity.
Publication Title
Advances in Intelligent Systems and Computing
Recommended Citation
Anastassiou, G. (2016). Bivariate left fractional polynomial monotone approximation. Advances in Intelligent Systems and Computing, 441, 1-13. https://doi.org/10.1007/978-3-319-30322-2_1
