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초록· 키워드
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Let f ∈ Cr ([−1, 1]), r ≥ 0 and let L∗ be a linear left fractional differential operator such that L∗ (f) ≥ 0 throughout [0, 1]. We can find a sequence of polynomials Qn of degree ≤ n such that L∗ (Qn) ≥ 0 over [0, 1], furthermore f is approximated left 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).
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참고문헌 (6)
참고문헌 신청
G. A. Anastassiou / 1985 / Monotone approximation with linear differential oper-ators / J. Approx. Theory 44 (4) : 391 ~ 393
G. A. Anastassiou / 1991 / Bivariate Monotone Approximation / Proc. Amer. Math 112 (4) : 959 ~ 964
G. A. Anastassiou / 1993 / Higher order monotone approximation with linear differential operators / Indian J. Pure Appl. Math 24 (4) : 263 ~ 266
H. H. Gonska / 1985 / Pointwise estimates for approximation by algebraic polynomials / Acta Math. Hungar 46 (3-4) : 243 ~ 254
K. Diethelm / 2010 / The Analysis of Fractional Differential Equations / Lecture Notes in Math-ematics 2004
G. A. Anastassiou / 1991 / Bivariate Monotone Approximation / Proc. Amer. Math 112 (4) : 959 ~ 964
G. A. Anastassiou / 1993 / Higher order monotone approximation with linear differential operators / Indian J. Pure Appl. Math 24 (4) : 263 ~ 266
H. H. Gonska / 1985 / Pointwise estimates for approximation by algebraic polynomials / Acta Math. Hungar 46 (3-4) : 243 ~ 254
K. Diethelm / 2010 / The Analysis of Fractional Differential Equations / Lecture Notes in Math-ematics 2004
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