Research Article

Some Approximation Properties of Series with Nonlinear Fourier Basis

Volume: 6 Number: 2 October 31, 2018
Hatice Aslan , Ali Güven
EN

Some Approximation Properties of Series with Nonlinear Fourier Basis

Abstract

The order of approximation of generalized de la Vallée Poussin means of series with nonlinear Fourier
basis was investigated in uniform and Hölder norms.

Keywords

Generalized de la Vallée Poussin mean,nonlinear Fourier basis,order of approximation

References

  1. [1] DeVore, R. A. and Lorentz, G., Constructive Approximation, Springer-Verlag. New York, 1993.
  2. [2] Holland, A. S. B., A survey of degree of approximation of continuous functions. SIAM Rev. 23 (1981), 344-379.
  3. [3] Huang, C. and Yang L., Approximation by the nonlinear Fourier basis. Sci. China Math. 54 (2011), 1207-1214.
  4. [4] Leindler, L., On summability of Fourier series. Acta Sci. Math. Szeged 29 (1968), 147-162.
  5. [5] Leindler, L., Meir, A. and Totik, V., On approximation of continuous functions in Lipschitz norms. Acta Math. Hung 45 (1985), 441-443.
  6. [6] Prössdorf, S., Zur konvergenz der Fourierreihen hölderstetiger funktionen. Math. Nachr. 69 (1975), 7-14.
  7. [7] Qian, T., Analytic signals and harmonic measures. J. Math. Anal. Appl. 314 (2006), 526-536.
  8. [8] Qian, T. and Chen, Q., Characterization of analytic phase signals. Comput. Math. Appl. 51 (2006), 1471-1482.
  9. [9] Stypinski, Z., On a generalization of the theorem of Prössdorf. Funct. Approx. Comment. Math. 7 (1979), 101-104.
  10. [10] Timan, A. F., Theory of approximation of functions of a real variable, Pergamon Press, 1963.
APA
Aslan, H., & Güven, A. (2018). Some Approximation Properties of Series with Nonlinear Fourier Basis. Mathematical Sciences and Applications E-Notes, 6(2), 22-27. https://doi.org/10.36753/mathenot.476784
AMA
1.Aslan H, Güven A. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. 2018;6(2):22-27. doi:10.36753/mathenot.476784
Chicago
Aslan, Hatice, and Ali Güven. 2018. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes 6 (2): 22-27. https://doi.org/10.36753/mathenot.476784.
EndNote
Aslan H, Güven A (October 1, 2018) Some Approximation Properties of Series with Nonlinear Fourier Basis. Mathematical Sciences and Applications E-Notes 6 2 22–27.
IEEE
[1]H. Aslan and A. Güven, “Some Approximation Properties of Series with Nonlinear Fourier Basis”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 22–27, Oct. 2018, doi: 10.36753/mathenot.476784.
ISNAD
Aslan, Hatice - Güven, Ali. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes 6/2 (October 1, 2018): 22-27. https://doi.org/10.36753/mathenot.476784.
JAMA
1.Aslan H, Güven A. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. 2018;6:22–27.
MLA
Aslan, Hatice, and Ali Güven. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, Oct. 2018, pp. 22-27, doi:10.36753/mathenot.476784.
Vancouver
1.Hatice Aslan, Ali Güven. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. 2018 Oct. 1;6(2):22-7. doi:10.36753/mathenot.476784