scholarly journals Inequalities of various metrics for the norms $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a,b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$ of differentiable functions on the real domain

2018 ◽  
Vol 26 (1) ◽  
pp. 48
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
Trigonometric Polynomials ◽  
The Real ◽  
Differentiable Functions ◽  
Real Domain

We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.

scholarly journals Bojanov-Naidenov problem for positive (negative) parts of differentiable functions on the real domain

2018 ◽  
Vol 26 (1) ◽  
pp. 25 ◽  
Author(s):  
V.V. Kameneva ◽  
V.A. Kofanov
Keyword(s):  
Extremal Problem ◽  
Local Norm ◽  
The Real ◽  
Differentiable Functions ◽  
Real Domain

We solve the extremal problem $$$\| x^{(k)}_{\pm} \|_{L_p[a,b]} \rightarrow \sup$$$, $$$k = 0, 1, ..., r-1$$$, over the set of pairs $$$(x, I)$$$ of functions $$$x\in W^r_{\infty} (\mathbb{R})$$$ and intervals $$$I = [a,b]$$$ with restrictions on the local norm of function $$$x$$$ and the measure of support $$$\mu \{ \mathrm{supp}_{[a,b]} x^{(k)}_{\pm} \}$$$.

scholarly journals Isometries between Spaces of Vector-Valued Differentiable Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Alireza Ranjbar-Motlagh
Keyword(s):  
Banach Space ◽  
Real Line ◽  
Convex Banach Space ◽  
Compact Interval ◽  
The Real ◽  
Strictly Convex ◽  
Differentiable Functions ◽  
Strictly Convex Banach Space ◽  
Vector Valued

This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space.

scholarly journals On some inequalities in various metrics for differentiable functions on real line

2021 ◽  
Vol 18 ◽  
pp. 123
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
The Real ◽  
Differentiable Functions

We obtain the estimates of the seminorms of Weil of the functions on the real line and their derivatives with the help of local $L_p$-norms of the functions and uniform norms of their highest derivatives.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real
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