Approximation of a Function and a Conjugate Function Belonging to Lip (α, γ) Class by(C,1)(E,q) Means

2013 ◽  
Vol 1 (6) ◽  
pp. 212
Author(s):  
Nigam Hare Krishna
Keyword(s):  
Conjugate Function ◽  
Approximation Of A Function

Singularity of the conjugate function for a point ?-detector

1973 ◽  
Vol 14 (1) ◽  
pp. 81-85
Author(s):  
A. M. Kol'chuzhkin ◽  
V. V. Uchaikin
Keyword(s):  
Conjugate Function ◽  
Point Detector

scholarly journals Conjugate function theory in weak∗ Dirichlet algebras

1974 ◽  
Vol 16 (4) ◽  
pp. 359-371 ◽  
Author(s):  
I.I. Hirschman ◽  
Richard Rochberg
Keyword(s):  
Function Theory ◽  
Conjugate Function

Some negative results for the interpolation monotone approximation of functions having a fractional derivative

2020 ◽  
pp. 122-127
Author(s):  
T. O. Petrova ◽  
I. P. Chulakov
Keyword(s):  
Fractional Derivative ◽  
Convex Function ◽  
Nondecreasing Function ◽  
Degree Of Approximation ◽  
Approximation Of Functions ◽  
Monotone Approximation ◽  
Convex Approximation ◽  
Negative Results ◽  
Positive Functions ◽  
Approximation Of A Function

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function $f є W^r [0,1]$ by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function $f є C^r [0,1] \cap \Delta^0$ where $\Delta^0$ is the set of positive functions on [0,1]. Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider $r є , r > 2$. In [8] is consider $r є , r > 2$. It was proved that for monotone approximation estimates of the form (1) are fails for $r є , r > 2$. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6]). In [5] is consider $r є , r > 2$. In [6] is consider $r є , r > 2$. It was proved that for convex approximation estimates of the form (1) are fails for $r є , r > 2$. In this paper the question of approximation of function $f є W^r \cap \Delta^1, r є (3,4)$ by algebraic polynomial $p_n є \Pi_n \cap \Delta^1$ is consider. The main result of the work generalize the result of work [8] for $r є (3,4)$.

scholarly journals Approximation of a Function Belonging to Lip (ɑ, θ, w) by (C, 1) (E, q)

2020 ◽  
Vol 37 (1-2) ◽  
pp. 80-85
Author(s):  
Smita Sonker ◽  
Alka Munjal ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Approximation Of A Function

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scholarly journals Approximation of a Function Belonging to Lip ((α, r) Class by Np,q. C1 Summability Method of its Fourier Series

2014 ◽  
Vol 14 (2) ◽  
pp. 117-122 ◽  
Author(s):  
JP Kushwaha ◽  
BP Dhakal
Keyword(s):  
Fourier Series ◽  
Science And Technology ◽  
Degree Of Approximation ◽  
Summability Method ◽  
Approximation Of A Function

In this paper, an estimate for the degree of approximation of a function belonging to Lip(α, r) class by product summability method Np.q.C1 of its Fourier series has been established. DOI: http://dx.doi.org/10.3126/njst.v14i2.10424 Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 117-122

scholarly journals On the Exponential Integrability of Conjugate Functions

2021 ◽  
Vol 27 (6) ◽  
Author(s):  
H. Gissy ◽  
S. Miihkinen ◽  
J. A. Virtanen
Keyword(s):  
Conjugate Function ◽  
Conjugate Functions ◽  
Exponential Integrability ◽  
Related Theorem

AbstractWe relate the exponential integrability of the conjugate function $${\tilde{f}}$$ f ~ to the size of the gap in the essential range of f. Our main result complements a related theorem of Zygmund.

scholarly journals Growth estimates for a Dirichlet series and its derivative

2020 ◽  
Vol 53 (1) ◽  
pp. 3-12
Author(s):  
S.I. Fedynyak ◽  
P.V. Filevych
Keyword(s):  
Continuous Function ◽  
Dirichlet Series ◽  
Half Plane ◽  
Conjugate Function ◽  
Nonnegative Sequence

Let $A\in(-\infty,+\infty]$, $\Phi$ be a continuous function on $[a,A)$ such that for every $x\in\mathbb{R}$ we have$x\sigma-\Phi(\sigma)\to-\infty$ as $\sigma\uparrow A$, $\widetilde{\Phi}(x)=\max\{x\sigma -\Phi(\sigma)\colon \sigma\in [a,A)\}$ be the Young-conjugate function of $\Phi$, $\overline{\Phi}(x)=\widetilde{\Phi}(x)/x$ for all sufficiently large $x$, $(\lambda_n)$ be a nonnegative sequence increasing to $+\infty$, $F(s)=\sum a_ne^{s\lambda_n}$ be a Dirichlet series absolutely convergent in the half-plane $\operatorname{Re}s<A$, $M(\sigma,F)=\sup\{|F(s)|\colon \operatorname{Re}s=\sigma\}$ and $G(\sigma,F)=\sum |a_n|e^{\sigma\lambda_n}$ for each $\sigma<A$. It is proved that if $\ln G(\sigma,F)\le(1+o(1))\Phi(\sigma)$, $\sigma\uparrow A$, then the inequality$$\varlimsup_{\sigma\uparrow A}\frac{M(\sigma,F')}{M(\sigma,F)\overline{\Phi}\,^{-1}(\sigma)}\le1$$holds, and this inequality is sharp. % Abstract (in English)

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