Kyungpook Mathematical Journal

  • 제56권1호
  • /
  • Pages.57-68
  • /
  • 2016
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

On Approximation by Matrix Means of the Multiple Fourier Series in the Hölder Metric

  • Deger, Ugur (Mersin University, Faculty of Science and Literature, Department of Mathematics)
  • 투고 : 2013.05.08
  • 심사 : 2015.10.07
  • 발행 : 2016.03.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, we shall give the degree of approximation for functions belonging to $H{\ddot{o}}lder$ class by matrix summability method of multiple Fourier series in the $H{\ddot{o}}lder$ metric.

키워드

참고문헌

  1. G. Alexits, Convergence problems of orthogonal series, New York: Pergamon Press, (1961).
  2. P. Chandra, On the generalized Fejer means in the metric of the Holder space, Math. Nachr., 109(1982), 39-45. https://doi.org/10.1002/mana.19821090105
  3. Y. S. Chow, On the Cesaro summability of double Fourier series, Tohoku Math. J., 5(1935), 277-283.
  4. E. Hille and J. D. Tamarkin, On the summability of Fourier series, Trans. Amer. Math. Soc., 34(1932), 757-783. https://doi.org/10.1090/S0002-9947-1932-1501662-X
  5. S. Lal, On the approximation of function f(x, y) belonging to Lipschitz class by matrix summability method of double Fourier series, Journal of the Indian Math. Soc., 78(1-4)(2011), 93-101.
  6. R. N. Mohapatra and P. Chandra, Degree of approximation of functions in the Holder metric, Acta Math. Hung., 41 (1-2)(1983), 67-76. https://doi.org/10.1007/BF01994063
  7. S. Prosdorff, Zur Konvergenz der Fourier reihen Holder Stetiger Funktionen, Math. Nachr., 69(1975), 7-14. https://doi.org/10.1002/mana.19750690102
  8. P. L. Sharma, On the harmonic summability of double Fourier series, Proc. Amer. Math. Soc., 91(1958), 979-986.
  9. A. I. Stepanets, The approximation of certain classes of differentiable periodic functions of two variables by Fourier sums, Ukrainian Mathematical Journal (Translated from Ukrainskii Matematieheskii Zhurnal, 25(5)(1973), 599-609), 26(1973), 498-506.
  10. A. I. Stepanets, Approximation of certain classes of periodic functions of two variables by linear methods of summation of their Fourier series, Ukrainian Mathematical Journal (Translated from Ukrainskii Matematieheskii Zhurnal, 26(2)(1974), 205-215), 26(1974), 168-179. https://doi.org/10.1007/BF01085721
  11. A. Zygmund, Trigonometric Series, Vol. II, Cambridge University Press, Cambridge, (1959).