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Sonker, Smita
- Approximation of Signals by Harmonic-Euler Triple Product Means
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Authors
Affiliations
1 Department of Mathematics, National Institute of Technology, Kurukshetra - 136119, IN
1 Department of Mathematics, National Institute of Technology, Kurukshetra - 136119, IN
Source
The Journal of the Indian Mathematical Society, Vol 88, No 1-2 (2021), Pagination: 176–186Abstract
Our paper deals with the approximation of signals by H1.Eθ.Eθ product means of Fourier and its conjugate series. New theorems based on H1.Eθ.Eθ product summability have been established and proved under general conditions. The established theorems extend, generalize and improve various existing results on summability of Fourier series and its conjugate series.Keywords
Degree of Approximation, Harmonic-Euler (H1.Eθ.Eθ) - Summability, Fourier Series, Conjugate Series, Lebesgue integral, Second Mean Value (SMV) Theorem
References
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- X. Z. Krasniqi and Deepmala, On approximation of functions belonging to some classes of functions by (N, pn, qn)(Eθ ) means of conjugate series of its Fourier series, Khayyam J. Math., 6 (1)(2020), 73 - 86.
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- Application of Almost Increasing Sequence for Absolute Riesz |Ñ, Pα,βN;δ ; Γ|K Summable Factor
Abstract Views :81 |
PDF Views:0
Authors
Smita Sonker
1,
Rozy Jindal
1
Affiliations
1 Department of Mathematics, NIT Kurukshetra, Kurukshetra, IN
1 Department of Mathematics, NIT Kurukshetra, Kurukshetra, IN
Source
The Journal of the Indian Mathematical Society, Vol 89, No 1-2 (2022), Pagination: 172–181Abstract
In this paper, we have proved a general theorem dealing with absolute Riesz |Ñ, P?,?N;? ; ?|K summablility by applying an almost increasing sequence. Also, some known results are also deduced.
Keywords
Absolute summability, infinite series, quasi-f-power increasing sequence, generalized Cesaro summability.References
- H. Bor, A new theorem on the absolute Riesz summability factors, Filomat, 28(8) (2014), 1537–1541.
- H. Bor, Some new results on infinite series and Fourier series, Positivity, 19(3) (2015), 467–473.
- H. Bor and H. Seyhan, On almost increasing sequences and its applications, Indian J. Pure Appl. Math., 30 (1999), 1041–1046.
- T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Sci., 3(1) (1957), 113–141.
- S. Sonker and A. Munjal, Absolute summability factor ? |C, 1; |k of Infinite series, Inter. J. Analysis Appl., 10(23), (2016), 1129–1136.
- S. Sonker and A. Munjal, Absolute ? |C, , ; |k summability of infinite series, J. Inequalities Appl., 168 (2017), 1–7.
- S. Sonker and A. Munjal, Application of quasi-f-power increasing sequences in Absolute ? |C, ; ; l|k summability, in Proc. International Conference for Computational Physics, Mathematics and Applications 2017.
- S. Sonker and A. Munjal, Absolute summability factor |N, pn|k of improper integral, Inter. J. Engg. and Tech., 9(3S) (2017), 457–462.
- S. Sonker and A. Munjal, Application of almost increasing sequence for absolute Riesz |Ñ, Pα,βN;δ ; Γ|K summable factor, Pertanika J. Sci. Tech., 262(2) (2018), 841–852.
- Approximation of Signal Belonging to W' (Lp, ξ(t)) Class by Generalized Cesaro-Euler (Cα,η.Eθ) Operator of Conjugate Fourier Series
Abstract Views :101 |
PDF Views:5
Authors
Affiliations
1 Department of Mathematics, National Institute of Technology Kurukshetra -136119, IN
1 Department of Mathematics, National Institute of Technology Kurukshetra -136119, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 187-198Abstract
In this paper, an attempt is made to establish a new theorem on approximation of signal belonging to W' (Lp, ξ(t)), (p ≥ 1), (t > 0) class by using generalized Ces`aro-Euler (Cα,η.Eθ) means of conjugate Fourier series. The established theorem extends, generalizes and improves previous results on summability of conjugate Fourier series for better convergence. In addition, product operators approximate more accurately than individual linear operators.
Keywords
Signal Approximation, Weighted Lipschitz WW' (Lp, ξ(t)), (P ≥ 1), (t 62; 0) Class, Ces`aro (Cα,η)-Mean, Euler (Eθ)-Mean, Ces`aro-Euler (Cα,η.Eθ) Product Mean, Conjugate Fourier Series, H¨older’s Inequality.References
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- Xh. Z. Krasniqi and Deepmala, On approximation of functions belonging to some classes of functions by (N, pn, qn)(E, θ) means of conjugate series of its Fourier series, Khayyam J. Math., 6 (1) (2020), 73—86.
- S. Lal and H. K. Nigam, Degree of approximation of conjugate of a function belonging to Lip (ξ (t), p) class by matrix summability means of conjugate Fourier series, Int. J. Math. Math. Sci., 27 (2001), 555—563.
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- M. L. Mittal, B. E. Rhoades and V. N. Mishra, Approximation of signals (functions) belonging to the weighted W(Lp, ξ(t), (p ≥ 1) class by linear operators, Intern. J. Math. Mathematical Sci., ID 5353 (2006), 1-–10.
- M. L. Mittal, B. E. Rhoades, S. Sonker and U. Singh, Approximation of signals of class Lip (α, p) by linear operator, Appl. Math. Computation, 217 (9) (2011), 4483–4489.
- H. K. Nigam, Approximation of conjugate function belonging to Lip (ξ (t), r) class by (C, 1) (E, 1) means, Intern. J. Math. Res., (2014), 15-–26.
- K. Qureshi, On the degree of approximation of a function belonging to weighted W(Lr, ξ(t)) class, Indian J. Pure Appl. Math., 13 (1982), 471–475.
- S. Sonker and U. Singh, Degree of approximation of the conjugate of signals (functions) belonging to Lip(α, r)-class by (C, 1)(E, q) means of conjugate trigonometric Fourier series, J. Inequal. Appl., 2012, 278, (2012).
- S. Sonker and P. Sangwan, Approximation of Signals by Harmonic-Euler Triple Product Means, J. Indian Math. Soc., 88 (1-2)(2021), 176–186.
- S. Sonker and P. Sangwan,Approximation of Fourier and its conjugate series by triple Euler product summability, J. Phys.: Conf. Ser., 1770, 012003 (2021), 1–10.
- A. Zygmund, Trigonometric Series Second Edition, Cambridge University Press, 1959.