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Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2020 / Cilt: 10 - Sayı: 1

DEGREE OF APPROXIMATION IN THE GENERALIZED LIPSCHITZ CLASS VIA (E, q)A- PRODUCT SUMMABILITY MEANS OF FOURIER SERIES

Arpita Anindita DAS
Bidu Bhusan JENA
Priyadarsini PARİDA
Umakanta MİSRA
Sayfa
53–62
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we have established a new theorem based on (E, q)A- product summability mean in order to estimate the degree of approximation of a function f ∈ Lip(ξ(t), r)

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Dealing with degree of approximation of Fourier series of functions of Lipchitz classes, some results have been established by Nigam [15] and Misra et al. [17].
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Temel Bulgular & Veri:Dealing with degree of approximation of Fourier series of functions of Lipchitz classes, some results have been established by Nigam [15] and Misra et al. [17].
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Sonuç & Katkı:In this paper, we have established a new theorem based on (E, q)A- product summability mean in order to estimate the degree of approximation of a function f ∈ Lip(ξ(t), r)
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

Dealing with degree of approximation of Fourier series of functions of Lipchitz classes, some results have been established by Nigam [15] and Misra et al. [17]. In this paper, we have established a new theorem based on (E, q)A- product summability mean in order to estimate the degree of approximation of a function f ∈ Lip(ξ(t), r)

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Bu Makaleye Atıf Yap

DAS, A. A., JENA, B. B., PARİDA, P., MİSRA, U. (2020). DEGREE OF APPROXIMATION IN THE GENERALIZED LIPSCHITZ CLASS VIA (E, q)A- PRODUCT SUMMABILITY MEANS OF FOURIER SERIES. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 10 - Sayı: 1, 53–62. https://ajindex.com/articles/327597

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Kaynakça (13)

  1. Aasma, A., Dutta, H. and Natarajan, P.N., (2017), An Introductory Course in Summability Theory, John Wiley and Sons, Hoboken, USA
  2. Deepmala, Mishra, L.N. and Mishra, V.N., (2014), Trigonometric Approximation of Signals 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 J. Math. Sci., 2, pp. 61-69
  3. Dutta, H. and Rhoades, B.E. (Eds.), (2016), Current Topics in Summability Theory and Applications, 1st ed., Springer, Singapore
  4. Das, S. and Dutta, H., (2018), Characterization of some matrix classes involving some sets with speed, Miskolc Math. Notes, 19, pp. 813-821
  5. Dutta, H. and Das, S., (2019), On variations via statistical convergence, J. Math. Anal. Appl., 472, pp. 133-147
  6. Hardy, G.H., (1949), Divergent Series, first ed., Oxford University Press, Oxford
  7. 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 J. Math., 31, pp. 279-288
  8. Mishra, V.N., Khan, H.H., Khatri, K. and 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, Bull. Math. Anal. Appl., 5, pp. 40-53
  9. Mishra, V.N., Khatri, K. and 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, J. Inequal. Appl., Article ID 296 doi: 10.1186/1029-242X-2012-296
  10. Mishra, V.N., Khatri, K. and 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, Mat. Vesnik, 66, pp. 155-164
  11. Mishra, V.N. and Mishra, L.N., (2012), Trigonometric approximation of signals (functions) in Lpnorm, International Journal of Contemp. Math. Sci., 7, pp. 909-918
  12. Mishra, V.N., Khatri, K., Mishra, L.N. and 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, J. Classical Anal., 5, pp. 91-105
  13. Mishra, L. N., Mishra, V.N., Khatri K. and Deepmala, (2014), On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(L r, ξ(t))(r ≥ 1)−