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Approximation of Signals in the Weighted Zygmund Class via Euler-Hausdorff Product Summability Mean of Fourier Series


Affiliations
1 Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India
2 Department of Mathematics, Gauhati University, Guwahati 781014, India
     

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Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class W(Zr(ω)) by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.

Keywords

Degree of Approximation, Weighted Zygmund Class, Trigonometric Fourier Series, Euler Mean, Hausdorff Mean.
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  • Approximation of Signals in the Weighted Zygmund Class via Euler-Hausdorff Product Summability Mean of Fourier Series

Abstract Views: 385  |  PDF Views: 1

Authors

A. A. Das
Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India
S. K. Paikray
Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India
T. Pradhan
Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India
H. Dutta
Department of Mathematics, Gauhati University, Guwahati 781014, India

Abstract


Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class W(Zr(ω)) by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.

Keywords


Degree of Approximation, Weighted Zygmund Class, Trigonometric Fourier Series, Euler Mean, Hausdorff Mean.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F22506