Degree of convergence of a function in generalized Zygmund space

Hare Krishna Nigam; Mohammad Mursaleen; Manoj Kumar Sah

doi:10.3934/mfc.2022029

Article Contents

2023, Volume 6, Issue 3: 484-499. Doi: 10.3934/mfc.2022029

This issue Previous Article Integral modification of Beta-Apostol-Genocchi operators Next Article Some new inequalities and numerical results of bivariate Bernstein-type operator including Bézier basis and its GBS operator

Degree of convergence of a function in generalized Zygmund space

1.
Department of Mathematics, Central University of South Bihar, Gaya, Bihar, India
2.
Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
3.
Department of Mathematics, Aligarh Muslim University, Aligarh, India

^*Corresponding author: M. Mursaleen
^*Corresponding author: M. Mursaleen

Received: February 2022

Revised: July 2022

Early access: August 19, 2022

Published online: August 19, 2022

Abstract / Introduction Full Text(HTML) Figure(2) / Table(2) Related Papers Cited by

Abstract

In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund $ (D^{h}_{g}N^{a,b}) $ transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Degree of convergence of function $ f $

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Figure 2. Degree of convergence of function $ f $

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Table 1. Degree of convergence of $f$ for different $n$

$n$	Degree of convergence of $f$
100	1.2575829
1000	1.1507909
10000	1.1082121
50000	1.0911295
100000	1.0854078
500000	1.0746045
1000000	1.0707630
.	.
.	.
$\infty$	1

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Table 2. Degree of convergence of $f$ for different $n$

$n$	Degree of convergence of $f$
100	3.8368
1000	3.5991
10000	3.4794
50000	3.4274
100000	3.4096
500000	3.3759
1000000	3.3639
10000000	3.3315
100000000	3.3073
.	.
.	.
$\infty$	3.1416

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References

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