On approximation of hexagonal Fourier series in the generalized Hölder metric

Hatice Aslan; Ali Güven

doi:10.15672/hujms.512908

Research Article

On approximation of hexagonal Fourier series in the generalized Hölder metric

Year 2020, Volume: 49 Issue: 3, 962 - 973, 02.06.2020

Hatice Aslan Ali Güven

https://doi.org/10.15672/hujms.512908

Abstract

Let $f$ be an $H$-periodic continuous function. The approximation order of the function $f$ by deferred Cesaro means of its hexagonal Fourier series is estimated in uniform and generalized H\"{o}lder metrics.

Keywords

Deferred Cesàro means, generalized Hölder class, hexagonal Fourier series

References

[1] R.P. Agnew, On deferred Cesàro means, Ann. of Math. 33 (3), 413–421, 1932.
[2] J. Bustamante and M.A. Jimenez, Trends in Hölder approximation, in: Approxima- tion, Optimization and Mathematical Economics, 81–95, Springer, 2001.
[3] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, 1993.
[4] B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16, 101–121, 1974.
[5] A. Guven, Approximation by means of hexagonal Fourier series in Hölder norms, J. Class. Anal. 1, 43–52, 2012.
[6] A. Guven, Approximation by (C, 1) and Abel-Poisson means of Fourier series on hexagonal domains, Math. Inequal. Appl. 16, 175–191, 2013.
[7] A. Guven, Approximation properties of hexagonal Fourier series in the generalized Hölder metric, Comput. Methods Funct. Theory, 13, 509–531, 2013.
[8] A. Guven, On approximation of hexagonal Fourier series, Azerb. J. Math. 8, 52–68, 2018.
[9] A.S.B. Holland, A survey of degree of approximation of continuous functions, SIAM Rev. 23, 344–379, 1981.
[10] L. Leindler, Generalizations of Prössdorf’s theorems, Studia Sci. Math. Hungar. 14, 431–439, 1979.
[11] L. Leindler, A relaxed estimate of the degree of approximation by Fourier series in generalized Hölder metric, Anal. Math. 35, 51–60, 2009.
[12] H. Li, J. Sun and Y. Xu, Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal. 46, 1653–1681, 2008.
[13] S. Prössdorf, Zur konvergenz der Fourierreihen hölderstetiger funktionen, Math. Nachr. 69, 7–14, 1975.
[14] J. Sun, Multivariate Fourier series over a class of non tensor-product partition do- mains, J. Comput. Math. 21, 53–62, 2003.
[15] A.F. Timan, Theory of Approximation of Functions of a Real Variable, Pergamon Press, 1963.
[16] Y. Xu, Fourier series and approximation on hexagonal and triangular domains, Con- str. Approx. 31, 115–138, 2010.
[17] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1959.

Year 2020, Volume: 49 Issue: 3, 962 - 973, 02.06.2020

Hatice Aslan Ali Güven

https://doi.org/10.15672/hujms.512908

Abstract

References

[1] R.P. Agnew, On deferred Cesàro means, Ann. of Math. 33 (3), 413–421, 1932.
[2] J. Bustamante and M.A. Jimenez, Trends in Hölder approximation, in: Approxima- tion, Optimization and Mathematical Economics, 81–95, Springer, 2001.
[3] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, 1993.
[4] B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16, 101–121, 1974.
[5] A. Guven, Approximation by means of hexagonal Fourier series in Hölder norms, J. Class. Anal. 1, 43–52, 2012.
[6] A. Guven, Approximation by (C, 1) and Abel-Poisson means of Fourier series on hexagonal domains, Math. Inequal. Appl. 16, 175–191, 2013.
[7] A. Guven, Approximation properties of hexagonal Fourier series in the generalized Hölder metric, Comput. Methods Funct. Theory, 13, 509–531, 2013.
[8] A. Guven, On approximation of hexagonal Fourier series, Azerb. J. Math. 8, 52–68, 2018.
[9] A.S.B. Holland, A survey of degree of approximation of continuous functions, SIAM Rev. 23, 344–379, 1981.
[10] L. Leindler, Generalizations of Prössdorf’s theorems, Studia Sci. Math. Hungar. 14, 431–439, 1979.
[11] L. Leindler, A relaxed estimate of the degree of approximation by Fourier series in generalized Hölder metric, Anal. Math. 35, 51–60, 2009.
[12] H. Li, J. Sun and Y. Xu, Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal. 46, 1653–1681, 2008.
[13] S. Prössdorf, Zur konvergenz der Fourierreihen hölderstetiger funktionen, Math. Nachr. 69, 7–14, 1975.
[14] J. Sun, Multivariate Fourier series over a class of non tensor-product partition do- mains, J. Comput. Math. 21, 53–62, 2003.
[15] A.F. Timan, Theory of Approximation of Functions of a Real Variable, Pergamon Press, 1963.
[16] Y. Xu, Fourier series and approximation on hexagonal and triangular domains, Con- str. Approx. 31, 115–138, 2010.
[17] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1959.

There are 17 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Hatice Aslan This is me 0000-0002-3486-4179 Ali Güven 0000-0001-8878-250X
Publication Date	June 2, 2020
Published in Issue	Year 2020 Volume: 49 Issue: 3

Cite

APA	Aslan, H., & Güven, A. (2020). On approximation of hexagonal Fourier series in the generalized Hölder metric. Hacettepe Journal of Mathematics and Statistics, 49(3), 962-973. https://doi.org/10.15672/hujms.512908
AMA	Aslan H, Güven A. On approximation of hexagonal Fourier series in the generalized Hölder metric. Hacettepe Journal of Mathematics and Statistics. June 2020;49(3):962-973. doi:10.15672/hujms.512908
Chicago	Aslan, Hatice, and Ali Güven. “On Approximation of Hexagonal Fourier Series in the Generalized Hölder Metric”. Hacettepe Journal of Mathematics and Statistics 49, no. 3 (June 2020): 962-73. https://doi.org/10.15672/hujms.512908.
EndNote	Aslan H, Güven A (June 1, 2020) On approximation of hexagonal Fourier series in the generalized Hölder metric. Hacettepe Journal of Mathematics and Statistics 49 3 962–973.
IEEE	H. Aslan and A. Güven, “On approximation of hexagonal Fourier series in the generalized Hölder metric”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, pp. 962–973, 2020, doi: 10.15672/hujms.512908.
ISNAD	Aslan, Hatice - Güven, Ali. “On Approximation of Hexagonal Fourier Series in the Generalized Hölder Metric”. Hacettepe Journal of Mathematics and Statistics 49/3 (June 2020), 962-973. https://doi.org/10.15672/hujms.512908.
JAMA	Aslan H, Güven A. On approximation of hexagonal Fourier series in the generalized Hölder metric. Hacettepe Journal of Mathematics and Statistics. 2020;49:962–973.
MLA	Aslan, Hatice and Ali Güven. “On Approximation of Hexagonal Fourier Series in the Generalized Hölder Metric”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, 2020, pp. 962-73, doi:10.15672/hujms.512908.
Vancouver	Aslan H, Güven A. On approximation of hexagonal Fourier series in the generalized Hölder metric. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):962-73.