Error estimation of the function by generalized Zygmund class using (T. C1) means of Fourier series

2021 ◽  
Author(s):  
Aradhana Dutt Jauhari
Keyword(s):  
Fourier Series ◽  
Error Estimation ◽  
Zygmund Class

scholarly journals On approximation in generalized Zygmund class

2019 ◽  
Vol 52 (1) ◽  
pp. 370-387
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Conjugate Function ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Product Method ◽  
Hausdorff Means

AbstractHere, we estimate the degree of approximation of a conjugate function {\tilde g} and a derived conjugate function {\tilde g'} , of a 2π-periodic function g \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

Approximation of Signals in the Weighted Zygmund Class Via Euler-hausdorff Product Summability Mean of Fourier Series

2020 ◽  
Vol 87 (1-2) ◽  
pp. 22
Author(s):  
A. A. Das ◽  
S. K. Paikray ◽  
T Pradhan ◽  
H. Dutta
Keyword(s):  
Fourier Series ◽  
Order Of Convergence ◽  
Approximation Of Functions ◽  
Zygmund Class ◽  
Approximation Of Signals

Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class <em>W(Z<sub>r</sub><sup>(ω)</sup>)</em> by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.

scholarly journals On Approximation of Signals in the Generalized Zygmund Class Using (E,r)(N,qn) Mean of Conjugate Derived Fourier Series

2020 ◽  
Vol 13 (5) ◽  
pp. 1325-1336
Author(s):  
Anwesha Mishra ◽  
Birupakhya Prasad Padhy ◽  
Umakanta Misra
Keyword(s):  
Fourier Series ◽  
Present Article ◽  
Degree Of Approximation ◽  
Zygmund Class ◽  
Approximation Of Signals ◽  
Approximation Of Function

In the present article, we have established a result on degree of approximation of function in the generalized Zygmund class Zl(m),(l ≥ 1) by (E,r)(N,qn)- mean of conjugate derived Fourier series.

scholarly journals Best approximation of conjugate of a function in generalized Zygmund

2019 ◽  
Vol 50 (4) ◽  
pp. 417-427
Author(s):  
Hare Krishna Nigam
Keyword(s):  
Fourier Series ◽  
Error Estimates ◽  
Best Approximation ◽  
Degree Of Approximation ◽  
Time Study ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
First Time

In this paper, we, for the very first time, study the error estimates of conjugate of a function ~g of g(2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq) product operatorof conjugate Fourier series. In fact, we establish two theorems on degree of approximation of afunction ~g of g (2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq)product means of its conjugate Fourier series. Our main theorem generalizes three previouslyknown results. Thus the results of [7], [8] and [26] become the particular cases of our Theorem2.1. Some corollaries are also deduced from our main theorem.

scholarly journals Approximation of function using generalized Zygmund class

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
H. K. Nigam ◽  
Mohammad Mursaleen ◽  
Supriya Rani
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Zygmund Space ◽  
Zygmund Class ◽  
Work Done ◽  
Appl Math ◽  
Approximation Of A Function ◽  
Derived Function ◽  
Approximation Of Function

AbstractIn this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approximation of a function g in the generalized Zygmund space and resolve the issue of these works. We also determine the best error approximation of the functions g and $g^{\prime }$ g ′ , where $g^{\prime }$ g ′ is a derived function of a 2π-periodic function g, in the generalized Zygmund class $X_{z}^{(\eta )}$ X z ( η ) , $z\geq 1$ z ≥ 1 , using matrix-Cesàro $(TC^{\delta })$ ( T C δ ) means of its Fourier series and its derived Fourier series, respectively. Theorem 2.1 of the present paper generalizes eight earlier results, which become its particular cases. Thus, the results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Nigam in Surv. Math. Appl. 5:113–122, 2010; Nigam in Commun. Appl. Anal. 14(4):607–614, 2010; Nigam and Sharma in Kyungpook Math. J. 50:545–556, 2010; Nigam and Sharma in Int. J. Pure Appl. Math. 70(6):775–784, 2011; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013; Shrivastava et al. in IOSR J. Math. 10(1 Ver. I):39–41, 2014) become particular cases of our Theorem 2.1. Several corollaries are also deduced from our Theorem 2.1.

Harmonic Detetion Algorithm Based on Identification and Simulation

2013 ◽  
Vol 340 ◽  
pp. 466-470
Author(s):  
Yun Jian Wang ◽  
Bei Bei Xie ◽  
Pei Liang Wang
Keyword(s):  
Fourier Series ◽  
Electric Power ◽  
Error Estimation ◽  
Detection Algorithm ◽  
Identification Accuracy ◽  
Harmonic Detection ◽  
Harmonic Model ◽  
Numerical Examples ◽  
Identification Error ◽  
Bounded Disturbance

A new harmonic detection algorithm is proposed in this paper. According to characteristics of the electric power harmonic, identified harmonic model is obtained based on Fourier series, and introduced a bounded disturbance in the model. When the parameter in the model is identified, firstly the interference value is estimated by the output error, and then the identification error is estimated and used it to update parameters of the model. By using the interference estimation and identification error estimation, the parameters convergence speed is accelerated and the identification accuracy is improved, numerical examples simulation verify this.

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