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### Sangwan, Paramjeet

- Approximation of Signals by Harmonic-Euler Triple Product Means

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1 Department of Mathematics, National Institute of Technology, Kurukshetra - 136119, IN

#### Authors

**Affiliations**

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: 176–186#### Abstract

Our paper deals with the approximation of signals by*H*product means of Fourier and its conjugate series. New theorems based on

_{1}.E^{θ}.E^{θ}*H*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.

_{1}.E^{θ}.E^{θ}#### Keywords

Degree of Approximation, Harmonic-Euler (*H*) - Summability, Fourier Series, Conjugate Series, Lebesgue integral, Second Mean Value (SMV) Theorem

_{1}.E^{θ}.E^{θ}#### References

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_{n}, q_{n})(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.
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- Approximation of Signal Belonging to W
^{'} (L^{p}, ξ(t)) Class by Generalized Cesaro-Euler (C^{α,η}.E^{θ}) Operator of Conjugate Fourier Series

^{'}(L^{p}, ξ(t)) Class by Generalized Cesaro-Euler (C^{α,η}.E^{θ}) Operator of Conjugate Fourier Series
Abstract Views :101 |
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1 Department of Mathematics, National Institute of Technology Kurukshetra -136119, IN

#### Authors

**Affiliations**

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: 187-198#### Abstract

In this paper, an attempt is made to establish a new theorem on approximation of signal belonging to W^{'} (L^{p}, ξ(t)), (p ≥ 1), (t > 0) class by using generalized Ces`aro-Euler (C^{α,η}.E^{θ}) 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^{'}(L

^{p}, ξ(t)), (P ≥ 1), (t 62; 0) Class, Ces`aro (C

^{α,η})-Mean, Euler (E

^{θ})-Mean, Ces`aro-Euler (C

^{α,η}.E

^{θ}) 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.
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- 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.
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- S. Sonker and P. Sangwan, Approximation of Signals by Harmonic-Euler Triple Product Means, J. Indian Math. Soc., 88 (1-2)(2021), 176–186.
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