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

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In this work, we shall give the degree of approximation for functions belongingto Holder class by matrix summability method of multiple Fourier series in the Holdermetric.

Abstract

In this work, we shall give the degree of approximation for functions belongingto Holder class by matrix summability method of multiple Fourier series in the Holdermetric.

참고문헌 (11)

  1. G. Alexits, "Convergence problems of orthogonal series" (1961), Pergamon Press
  2. P. Chandra, "On the generalized Fejer means in the metric of the HÄolder space", Math. Nachr., 109, pp.39~45 (1982)
  3. Y. S. Chow, "On the Cesaro summability of double Fourier series", Tohoku Math. J., 5, pp.277~283 (1935)
  4. E. Hille, "On the summability of Fourier series", Trans. Amer. Math. Soc., 34, pp.757~783 (1932)
  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), pp.93~101 (2011)
  6. R. N. Mohapatra, "Degree of approximation of functions in the HÄolder metric", Acta Math. Hung., 41(1-2), pp.67~76 (1983)
  7. S. PrÄosdorff, "Zur Konvergenz der Fourier reihen HÄolder Stetiger Funktionen", Math. Nachr., 69, pp.7~14 (1975)
  8. P. L. Sharma, "On the harmonic summability of double Fourier series", Proc. Amer. Math. Soc., 91, pp.979~986 (1958)
  9. A. I. Stepanets, "The approximation of certain classes of differentiable periodic func-tions of two variables by Fourier sums", Ukrainian Mathematical Journal, 26, pp.498~506 (1973)
  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, 26, pp.168~179 (1974)
  11. A. Zygmund, "Trigonometric Series, Vol. II" (1959), Cambridge University Press

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