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Sangwan, Paramjeet
- 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
- P. Chandra, On the degree of approximation of a class of functions by means of Fourier series, Acta Math. Hungar., 52 (3-4)(1988), 199 - 205.
- X. Z. Krasniqi, On the degree of approximation of a function by (C, 1)(E, q) means of its Fourier-Laguerre series, Int. J. Analysis Appl., 1 (1)(2013), 33 - 39.
- 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.
- S. Lal and H. K. Nigam, On almost (N, p, q) summability of conjugate Fourier series, Int. J. Math. Mathematical Sc., 25 (6)(2001), 365 - 372.
- S. Lal and J. K. Kushwaha, Degree of approximation of lipschitz function by product summability method, Int. Math. Forum, 4 (43)(2009), 2101 - 2107.
- M. L. Mittal and G. Prasad, On a sequence of Fourier coefficients, Indian J. Pure Appl. Math, 23 (3)(1992), 235 - 241.
- M. L. Mittal and U. Singh, T· C1 summability of a sequence of Fourier coefficients, Appl. Math. Comput., 204 (2)(2008), 702 - 706.
- R. Mohanty and M. Nanda, On the behaviour of Fourier coefficients, Proc. Amer. Math. Soc., 1 (1954), 79 - 84.
- M. Mursaleen and A. Alotaibi, Generalized matrix summability of a conjugate derived Fourier series, Jour. Ineq. Appl., (2017) 2017: 273.
- K. Qureshi, On the degree of approximation to a function belonging to weighted W(L(r), (t)) Class, Indian J. Pure App. Math, 13 (4)(1982), 471 - 475.
- B. N. Sahney and D. S. Goel, On the degree of approximation of continuous functions, Ranchi Univ. Math. J, 4. (1973), 50 - 53.
- S. Sonker, Approximation of Functions by means of its Fourier-Laguerre series, Proceeding of ICMS-2014, 1. (1)(2014), 125 - 128.
- S. Verma and K. Saxena, A study on (H, 1)(E, q) product summability of Fourier series and its Conjugate series, Math. Theory and Model., 7. (5) (2017).
- A. Zygmund, Trigonometric series, Cambridge University Press, 2002.
- 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
- H. H. Khan, On the degree of approximation of functions belonging to the class Lip(α, p), Indian J. Pure Appl. Math., 5 (2) (1974), 132–136.
- X. Z. Krasniqi, On the degree of approximation of functions belonging to the Lipschitz class by (E, q)(C, α, β) means, Khayyam J. Math. 1 (2) (2015), 243-–252.
- 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.
- L. Leindler, Trigonometric approximation in Lp norm, J. Math. Anal. Appl., 302(2005), 129–136.
- V. N. Mishra, K. Khatri and L. N. Mishra, Approximation of functions belonging to Lip(ξ(t), r) class by (N, pn)(E, q) summability of conjugate series of Fourier series, J. Inequal. Appl., Vol. 2012(1), (2012), Art. 296.
- M. L. Mittal, B. E. Rhoades, V. N. Mishra, S. Priti and S. S. Mittal, Approximation of functions belonging to Lip (ξ (t), p), (p ≥ 1) class by means of conjugate Fourier series using linear operators, Indian J. Math., 47 (2005), 217-–229.
- 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.