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Trigonometric Approximation of Signals (Functions) Belonging to the Lip(ξ(t),r),(r>1)-Class by (E,q) (q>0)-Means of the Conjugate Series of Its Fourier Series

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DOI: 10.4236/apm.2013.33050    2,815 Downloads   5,000 Views   Citations

ABSTRACT

Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα, Lip(α,r), Lip(ξ(t),r) and W(Lr,ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to Lip(ξ(t),r) class by (E,q) summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

V. Mishra, H. Khan, I. Khan, K. Khatri and L. Mishra, "Trigonometric Approximation of Signals (Functions) Belonging to the Lip(ξ(t),r),(r>1)-Class by (E,q) (q>0)-Means of the Conjugate Series of Its Fourier Series," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 353-358. doi: 10.4236/apm.2013.33050.

References

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