Spline left fractional monotone approximation involving left fractional differential operators
2015; University of La Frontera; Volume: 17; Issue: 1 Linguagem: Inglês
10.4067/s0719-06462015000100005
ISSN0719-0646
Autores Tópico(s)Nonlinear Differential Equations Analysis
ResumoLet f ∈ C s ([-1, 1]), s∈ N and L * be a linear left fractional differential operator such that L * (f) ≥ 0 on [0, 1].Then there exists a sequence Q n , n ∈ N of polynomial splines with equally spaced knots of given fixed order such thatFurthermore f is approximated with rates fractionally and simultaneously by Q n in the uniform norm.This constrained fractional approximation on [-1, 1] is given via inequalities invoving a higher modulus of smoothness of f (s) . RESUMENSea f ∈ C s ([-1, 1]), s∈ N y L * un operador diferencial fraccionario lineal izquierdo tal que L * (f) ≥ 0 en [0, 1].. Entonces, existe una sucesión Q n , n ∈ N de splines polinomiales con nodos equiespaciados de un orden fijo dado tal que L * (Q n ) ≥ 0 en [0, 1].Además, f se aproxima con velocidades fraccionales y simultáneamente por Q n en la norma uniforme.Esta aproximación fraccional restringida a [-1, 1] se encuentra por medio de desigualdades que involucran un módulo alto de suavidad de f (s) .
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