Univariate right fractional polynomial high order monotone approxi mation

• Autorzy: Anastassiou G. A.
• Języki publikacji: EN

Abstrakty

EN

Let (…) and let L* be a linear right fractional differential operator such that L*(f) ≥ 0 throughout [-1, 0]. We can find a sequence of polynomials Qn of degree ≤ n such that L*(Qn)≥ 0 over [-1, 0], furthermore f is approximated right fractionally and simultaneously by Qn on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for f(r).

Słowa kluczowe

EN

monotone approximation; right Caputo fractional derivative; right fractional linear differential operator; higher order modulus of smoothness

PL

aproksymacja monotoniczna; pochodna rzędu ułamkowego Caputo

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 1
• Strony: 1--10
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Anastassiou G. A.

• Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.

Bibliografia

• [1] G. A. Anastassiou, Bivariate monotone approximation, Proc. Amer. Math. Soc. 112(4) (1991), 959–963.
• [2] G. A. Anastassiou, Higher order monotone approximation with linear differential operators, Indian J. Pure Appl. Math. 24(4) (1993), 263–266.
• [3] G. A. Anastassiou, O. Shisha, Monotone approximation with linear differential operators, J. Approx. Theory 44 (1985), 391–393.
• [4] A. M. A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives, Elect. J. Theor. Phys. 3(12) (2006), 81–95.
• [5] H. H. Gonska, E. Hinnemann, Pointwise estimated for approximation by algebraic polynomials, Acta Math. Hungar. 46 (1985), 243–254.
• [6] O. Shisha, Monotone approximation, Pacific J. Math. 15 (1965), 667–671.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.