Applications of Some Classes of Sequences on Approximation of Functions (Signals) by Almost Generalized Nörlund Means of Their Fourier Series

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Xhevat Z. Krasniqi, Applications of Some Classes of Sequences on Approximation of Functions (Signals) by Almost Generalized Nörlund Means of Their Fourier Series, Int. J. Anal. Appl., 9 (1) (2015), 45-53.

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Xhevat Z. Krasniqi

Abstract

In this paper, using rest bounded variation sequences and head bounded variation sequences, some new results on approximation of functions (signals) by almost generalized Nörlund means of their Fourier series are obtained. To our best knowledge this the first time to use such classes of sequences on approximations of the type treated in this paper. In addition, several corollaries are derived from our results as well as those obtained previously by others.

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References

  1. D. Borwein, On product of sequences, J. London Math. Soc., 33 (1958), 352-357.
  2. J. P. King, Almost summable sequence, Proc. Amer. Math. Soc. 17 (1966), 1219-1225.
  3. G. G. Lorentz, A contribution to the theory of divergent series, Acta Math. 80 (1948), 167- 190.
  4. L. Leindler, On the uniform convergence and boundedness of a certain class of sine series, Anal. Math. 27 (2001), 279-285.
  5. L. McFadden, Absolute N ¨orlund summability, Duke Math. J. 9 (1942), 168-207.
  6. V. N. Mishra et al , On the degree of approximation of signals Lip(α, r), (r ≥ 1) class by almost Riesz means of its Fourier series, Journal of Classical Analysis 4 (2014), 79-87.
  7. J. G. Proakis, Digital Communications, McGraw-Hill, New York, 1995.
  8. E. Z. Psariks, G. V. Moustakids, An L2 -based method for the design of 1 D Zero phase FIR Digital Filters, Stockticker, IEEE transactions on Circuit and systems, Fundamental Theory & Applications, 4, 7 (1997), 591-601.
  9. P. L. Sharma and K. Qureshi, On the degree of approximation of a periodic function f by almost Riesz means, Ranchi Univ. Math. J. 11 (1980), 29-33 (1982).
  10. S. P. Zhou et al, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, arXiv:math/0611805v1 [math.CA] 27 Nov 2006.