Left general fractional monotone approximation theory

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

Abstrakty

EN

We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative over I, and furthermore f is approximated uniformly by Qₙ over [a,b].
The degree of this constrained approximation is given by an inequality using the first modulus of continuity of $f^{(p)}$. We finish with applications of the main fractional monotone approximation theorem for different g. On the way to proving the main theorem we establish useful related general results.

Kategorie tematyczne

• 26A33: Fractional derivatives and integrals
• 41A29: Approximation with constraints
• 41A10: Approximation by polynomials
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2016
• Tom: 43
• Numer: 1
• Strony: 117-131

Daty

wydano

2016

Twórcy

autor

George A. Anastassiou

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

Identyfikatory

DOI

10.4064/am2264-12-2015