Spline left fractional monotone approximation involving left fractional differential operators
- George A. Anastassiou ganastss@memphis.edu
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https://doi.org/10.4067/S0719-06462015000100005Abstract
Let f ∈ Cs ([−1, 1]), s∈ IN and L∗ be a linear left fractional differential operator such that L∗(f) ≥ 0 on [0,1]. Then there exists a sequence Qn, n ∈ IN of polynomial splines with equally spaced knots of given fixed order such that L∗ (Qn) ≥ 0 on [0, 1]. Furthermore f is approximated with rates fractionally and simultaneously by Qn in the uniform norm. This constrained fractional approximation on [−1, 1] is given via inequalities invoving a higher modulus of smoothness of f(s).
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Published
2015-03-01
How to Cite
[1]
G. A. Anastassiou, “Spline left fractional monotone approximation involving left fractional differential operators”, CUBO, vol. 17, no. 1, pp. 65–73, Mar. 2015.
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