On approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space Lp→,p ∈ [1,∞]2
Keywords:summation methods, Fourier series, order of convergence
In this paper, we study the approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space Lp, p ∈ [1,∞]2 using double Karamata Kλ,μ means.
A. Benedek and R. Panzone, “The space LP, with mixed norm”, Duke Mathematical Journal, vol. 28, no. 3, pp. 301-324, 1961. https://doi.org/10.1215/s0012-7094-61-02828-9
S. Lal and A. Mishra, “Approximation of function f(x, y) belonging to generalized lipschitz class by (N, Pm, Qn) method of the doublé Fourier series”, Bulletin of Mathematical Analysis and Applications, vol. 7, pp. 28-36, 2015.
B. Landon, H. Carley and R. N. Mohapatra, “Approximation by the (Kλ) means of Fourier series and conjugate series of functions in Hα,p”, Applicable Analysis and Discrete Mathematics, vol. 14, pp. 800-818, 2020.
H.K Nigam and Md Hadish, “Approximation of a function in Holder class using double Karamata (Kλμ) method”, European journal of pure and applied mathematics, vol. 13, pp. 567-578, 2020. https://doi.org/10.29020/nybg.ejpam.v13i3.3663
P. Sadangi, Degree of convergence of function in the Holder metric, Ph. D. Thesis, Utkal University, 2006.
V. Vuckovic, “The summability of Fourier series by Karamata methods”, Mathematische Zeitschrift, vol. 89, pp. 192-195, 1965.
R.G Vyas, “Convolution product of functions of generalized Wiener class”, The Mathematics Student, vol. 90, 2021. https://doi.org/10.1515/gmj-2015-0011
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