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## Applicationes Mathematicae

2016 | 43 | 1 | 117-131
Tytuł artykułu

### Left general fractional monotone approximation theory

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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.
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Tom
Numer
Strony
117-131
Opis fizyczny
Daty
wydano
2016
Twórcy
• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
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