Nonlinear Functional Analysis and Applications

  • 제28권4호
  • /
  • Pages.1035-1049
  • /
  • 2023
  • /
  • 1229-1595(pISSN)
  • /
  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
권호 표지
DOI QR코드

DOI QR Code

DEGREE OF APPROXIMATION OF A FUNCTION ASSOCIATED WITH HARDY-LITTLEWOOD SERIES IN WEIGHTED ZYGMUND W(Z(𝜔)r)-CLASS USING EULER-HAUSDORFF SUMMABILITY MEANS

  • Tejaswini Pradhan (Department of Mathematics, Kalinga University) ;
  • G V V Jagannadha Rao (Department of Mathematics, Kalinga University)
  • 투고 : 2023.04.19
  • 심사 : 2023.06.27
  • 발행 : 2023.12.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z(𝜔)r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.

키워드

참고문헌

  1. A.A. Das, S.K. Paikray, T. Pradhan and H. Dutta, Approximation of signals in the weighted Zygmund class via Euler-Huasdroff product summabilitymean of Fourier series, J. Indian Math. Soc., 87(1-2) (2020), 22-36.
  2. G.H. Hardy, Divergent Series, Oxford University Press, First Edition, 1949.
  3. W.A. Hurwitz and L.L. Silverman, On the consistency and equivalence of certain definitions of summability, Trans. Amer. Math. Soc., 18 (1917), 1-20.
  4. B.B. Jena, S.K. Paikray and M. Mursaleen, On degree of approximation of Fourier series based on a certain class of product deferred summability means, J. Inequal. Appl., 2023(18) (2023), doi.org.10.1186/s13660-023-02927-z.
  5. S. Lal and A. Mishra, Euler-Hausdorff matrix summability operator and trigonometric approximation of the conjugate of a function belonging to the generalized Lipschitz class, J. Inequal. Appl., 59 (2013), https://doi.org/10.1186/1029-242X-2013-59.
  6. S. Lal and Shireen, Best approximation of functions of generalized Zygmund class by Matrix-Euler summability mean of Fourier series, Bull. Math. Anal. Appl., 5(4) (2013), 1-13.
  7. L. Leindler, Strong approximation and generalized Zygmund class, Acta Sci. Math., 43 (1981), 301-309.
  8. M. Misra, P. Palo, B.P. Padhy, P. Samanta and U.K. Misra, Approximation of Fourier series of a function of Lipchitz class by product means, J. Adv. Math., 9(4) (2014), 2475-2483.
  9. F. Moricz, Enlarged Lipschitz and Zygmund classes of functions and Fourier transforms, East J. Approx., 16(3) (2010), 259-271.
  10. F. Moricz and J. Nemeth, Generalized Zygmund classes of functions and strong approximation of Fourier series, Acta. Sci. Math., 73 (2007), 637-647.
  11. H.K. Nigam and K. Sharma, On (E,1)(C,1) summability of Fourier series and its conjugate series, Int. J. Pure Appl. Math., 82(3) (2013), 365-375.
  12. B.P. Padhy, P. Baliarsingh, L. Nayak and H. Dutta, Approximation of Functions belonging to Zygmund Class Associated with Hardy-Littlewood Series using Riesz Mean, Appl. Math. Inform. Sci., 16(2) (2022), 243-248.
  13. T. Pradhan, S.K. Paikray, A.A. Das and H. Dutta, On approximation of signals in the generalized Zygmund class via (E, 1)(${\bar{N}}$, p) summability means of conjugate Fourier series, Proyecciones J. Math., 38(5) (2019), 981-998.
  14. T. Pradhan, S.K. Paikray and U. Misra, Approximation of signals belonging to generalized Lipschitz class using (${\bar{N}}$, p, q)(E, s)-summability mean of Fourier series, Cogent Math., 3(1) (2016), 1-9.
  15. T. Pradhan, S.K. Paikray and U.K. Misra, Approximation of signals using generalized Zygmund class using (E, 1)(${\bar{N}}$, pn) summability means of Fourier series, Indian Soc. Indust. Appl. Math., 10(1) (2019), 152-164.
  16. M.V. Singh, M.L. Mittal and B.E. Rhoades, Approximation of functions in the generalized Zygmund class using Hausdorff means, J. Inequal. Appl., 101 (2017), DOI 10.1186/s13600-017-1361-8.
  17. E.C. Titechmalch, The Theory of Functions, Oxford University Press, 1939.
  18. A. Zygmund, Trigonometric series, 2nd rev. ed., I, Cambridge Univ. Press, Cambridge, 51, 1968.