scholarly journals Generalization of A.A. Ligun's inequality to $L_q$, $q \in [0, 1)$ spaces

2021 ◽  
Vol 16 ◽  
pp. 111
Author(s):  
V.A. Kofanov
Keyword(s):  
Periodic Functions ◽  
Derivatives Of

We obtain generalization of the known A.A. Ligun's inequality to non-normed $L_q$-spaces for derivatives of periodic functions.

Order-Preserving Approximations to Successive Derivatives of Periodic Functions by Iterated Splines

1988 ◽  
Vol 25 (6) ◽  
pp. 1442-1452 ◽  
Author(s):  
M. J. Shelley ◽  
G. R. Baker
Keyword(s):  
Periodic Functions ◽  
Derivatives Of

scholarly journals Inequalities for norms of derivatives of non-periodic functions with non-symmetric constraints on higher derivatives

2012 ◽  
Vol 20 ◽  
pp. 99
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
Periodic Functions ◽  
Higher Derivatives ◽  
Derivatives Of

For non-periodic functions $x \in L^r_{\infty}(\mathbb{R})$ defined on the whole real line we established the analogs of certain inequality of V.F. Babenko.

scholarly journals On optimal interval quadrature formulae on classes of differentiable periodic functions

2021 ◽  
Vol 15 ◽  
pp. 16
Author(s):  
V.F. Babenko ◽  
D.S. Skorokhodov
Keyword(s):  
Quadrature Formula ◽  
Invariant Set ◽  
Periodic Functions ◽  
Quadrature Formulae ◽  
Optimal Interval ◽  
Arbitrary Permutation ◽  
Derivatives Of

We solved the problem about the best interval quadrature formula on the class $W^r F$ of differentiable periodic functions with arbitrary permutation-invariant set $F$ of derivatives of order $r$. We proved that the formula with equal coefficients and $n$ node intervals, which have equidistant middle points, is the best on given class.

scholarly journals The best polynomial approximation, derivatives of fractional order, and widths of classes of functions in $L_2$

2016 ◽  
Vol 24 ◽  
pp. 10
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Fractional Order ◽  
Polynomial Approximation ◽  
Fractional Derivatives ◽  
Periodic Functions ◽  
Best Polynomial Approximation ◽  
Alpha Beta ◽  
Derivatives Of

On the classes of $2\pi$-periodic functions ${\mathcal{W}}^{\alpha} (K_{\beta}, \Phi)$, where $\alpha, \beta \in (0;\infty)$, defined by $K$-functionals $K_{\beta}$, fractional derivatives of order $\alpha$, and majorants $\Phi$, the exact values of different $n$-widths have been computed in the space $L_2$.

A note on fractional-order derivatives of periodic functions

Automatica ◽  
2010 ◽  
Vol 46 (5) ◽  
pp. 945-948 ◽  
Author(s):  
Mohammad Saleh Tavazoei
Keyword(s):  
Fractional Order ◽  
Periodic Functions ◽  
Derivatives Of

Inequalities for norms of derivatives of periodic functions

1983 ◽  
Vol 33 (3) ◽  
pp. 196-199
Author(s):  
A. A. Ligun
Keyword(s):  
Periodic Functions ◽  
Derivatives Of
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