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Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2019 / Cilt: 9 - Sayı: 4

DEGREE OF APPROXIMATION BY PRODUCT (N, pn, qn)(E, q) SUMMABILITY OF FOURIER SERIES OF A SIGNAL BELONGING TO Lip(α, r)-CLASS

Arpita Anindita DAS
Bidu Bhusan JENA
M. DASH
Umakanta MİSRA
Sayfa
901–908
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper a new theorem has been established on (N, pn, qn)(E, q)- summability of Fourier series of a function belonging to f ∈ Lip(α, r) class that generalizes several known results.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Approximation of periodic functions by different linear summation methods have been studied by many researchers.
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Temel Bulgular & Veri:Further, for sharpening the estimate of errors out of the approximations several product summability methods were introduced by different investigators.
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Sonuç & Katkı:In this paper a new theorem has been established on (N, pn, qn)(E, q)- summability of Fourier series of a function belonging to f ∈ Lip(α, r) class that generalizes several known results.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

Approximation of periodic functions by different linear summation methods have been studied by many researchers. Further, for sharpening the estimate of errors out of the approximations several product summability methods were introduced by different investigators. In this paper a new theorem has been established on (N, pn, qn)(E, q)- summability of Fourier series of a function belonging to f ∈ Lip(α, r) class that generalizes several known results.

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Bu Makaleye Atıf Yap

DAS, A. A., JENA, B. B., DASH, M., MİSRA, U. (2019). DEGREE OF APPROXIMATION BY PRODUCT (N, pn, qn)(E, q) SUMMABILITY OF FOURIER SERIES OF A SIGNAL BELONGING TO Lip(α, r)-CLASS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 4, 901–908. https://ajindex.com/articles/327479

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Kaynakça (11)

  1. Deepmala, Mishra, L. N., Mishra, V. N., (2014), Trigonometric Approximation of Signals (Functions) belonging to the W(Lr, ξ(t)),(r ≥ 1)− class by (E, q) (q > 0)-means of the conjugate series of its Fourier series, Global Journal of Mathematical Sciences, 2, pp. 61-69
  2. Hardy, G. H., (1949), Divergent Series, first ed., Oxford University Press, Oxford
  3. Lal, S., (2000), On degree of approximation of conjugate of a function belonging to weighted W(Lp, ξ(t)) class by matrix summability mean of conjugate fourier series, Tamkang Journal of Mathematics, 31, pp. 279-288
  4. Mishra, V. N., Khan, H. H., Khatri, K., Mishra, L. N., (2013), Degree of approximation of conjugate of signals (functions) belonging to the generalized weighted Lipschitz W0 (Lr, ξ(t)),(r ≥ 1)-class by (C, 1)(E, q)-means of conjugate trigonometric Fourier series, Bulletin of Mathematical Analysis and Applications, 5, pp. 40-53
  5. Mishra, V. N., Khatri, K., Mishra, L. N., (2012), Approximation of functions belonging to Lip(ξ(t), r) class by (N, pn)(E, q)-summability of conjugate series of Fourier series, Journal of Inequalities and Applications, Article ID 296 doi: 10.1186/1029-242X-2012-296
  6. Mishra, V. N., Khatri, K., Mishra, L. N., (2014), Approximation of Functions belonging to the generalized Lipschitz Class by C 1.Np-summability method of conjugate series of Fourier series, Matematiˇcki Vesnik, 66, pp. 155-164
  7. Mishra, V. N., Mishra, L. N., (2012), Trigonometric approximation of signals (functions) in Lp-norm, International Journal of Contemporary Mathematical Sciences, 7, pp. 909 - 918
  8. Mishra, V. N., Khatri, K., Mishra, L. N., Deepmala, (2014), Trigonometric approximation of periodic Signals belonging to generalized weighted Lipschitz W0 (Lr, ξ(t)),(r ≥ 1)-class by N¨orlund-Euler (N, pn)(E, q) operator of conjugate series of its Fourier series, Journal of Classical Analysis, 5, pp. 91-105, doi:10.7153/jca-05-08
  9. Mishra, L. N., Mishra, V. N., Khatri, K., Deepmala, (2014), On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(L r, ξ(t))(r ≥ 1)− class by matrix (C 1.Np) Operator of conjugate series of its Fourier series, Applied Mathematics and Computation, 237, pp. 252-263
  10. Misra, M., Palo, P., Padhy, B. P., Samanta, P., Misra, U. K., (2014), Approximation of Fourier series of a function of Lipschitz class by product means, Journal of Advances in Mathematics, 9, pp. 2475-2484
  11. Nigam, H. K., (2013), On approxima