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Approximation of Signal Belonging to W' (Lp, ξ(t)) Class by Generalized Cesaro-Euler (Cα,η.Eθ) Operator of Conjugate Fourier Series
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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.
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- 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.
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