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Groups of Deviations of the Fourier Series in Generalized Hölder Spaces

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Ukrainian Mathematical Journal Aims and scope

We study the rate of convergence of the values of analogs of the functionals of strong approximation of Fourier series in generalized L-Hölder spaces.

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References

  1. S. Prössdorf, “Zur Konvergens der Fourierreihen Hölderstetiger,” Math. Nachr., 69, 7–14 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  2. L. Leindler, “Generalizations of Prössdorf’s theorems,” Stud. Math. Hung., 14, 431–439 (1979).

    MATH  Google Scholar 

  3. R. Mohapatra and P. Chandra, “Degree of approximation of functions in the Hölder metric,” Acta Math. Hung., 41, No. 1-2, 67–74 (1983).

    Article  MATH  Google Scholar 

  4. R. A. Lasuriya, “On the approximation of periodic functions by linear means of the Fourier sums in a generalized Hölder metric,” Dokl. Adyg. Mezhdunarod. Akad. Nauk, 5, No. 1, 24–39 (2000).

    Google Scholar 

  5. R. A. Lasuriya, Approximation of Functions in a Generalized Hölder Metric [in Russian], Abkhaz. Gos. Univ., Sukhum (2001).

    MATH  Google Scholar 

  6. R. A. Lasuriya, “On the approximation of functions given on the entire real axis by Fej´er-type operators in a generalized Hölder metric,” Mat. Zametki, 181, No. 4, 547–552 (2007).

    Article  MathSciNet  Google Scholar 

  7. B. R. Draganov, “Simultaneous approximation of functions by Fejer-type operators in a generalized Hölder norm,” E. J. Approxim., 14, 439–449 (2008).

    MathSciNet  MATH  Google Scholar 

  8. R. N. Mohapatra and B. Szal, Degree of Convergence of an Integral Operator, arXiv: 1205.5870 V1 [math. CA] (2012).

  9. P. Chandra, “Degree of approximation of functions in the Hölder metric by Borel’s means,” J. Math. Anal. Appl., 149, 236–246 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  10. G. Das, T. Ghosh, and B. K. Ray, “Degree of approximation of functions by their Fourier series in the generalized Hölder metric,” Proc. Indian Acad. Sci. (Math. Sci.), 106, 139–153 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. V. Zhuk, “Approximation of periodic functions in the Hölder-type metric by Fourier sums and Riesz means,” Zap. Nauch. Sem. POMI, 350, 70–88 (2007).

    Google Scholar 

  12. L. Leindler, “A relaxed estimate of the degree of approximation by Fourier series in generalized Hölder metric,” Anal. Math., 35, 51–60 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  13. B. A. Landon, Degree of Approximation of Hölder Continuous Functions, PhD Thesis in Mathematics, Orlando, USA (2008).

  14. W. Lenski and B. Szal, “On the approximation of functions by matrix means in the generalized Hölder metric,” Banach Center Publications, 79, 119–129 (2008).

    MATH  Google Scholar 

  15. A. Nath, “Degree of approximation by matrix mean in a generalized Hölder metric,” J. Orissa Math. Soc., 30, No. 2, 81–92 (2011).

    Google Scholar 

  16. G. Das, B. K. Ray, and P. Sadangi, “Approximation by the K λ means of Fourier series and conjugate series in the Hölder metric,” J. Orissa Math. Soc., 30, No. 2, 49–66 (2011).

    MathSciNet  Google Scholar 

  17. T. Singh, “Degree of approximation of functions in the generalized Hölder metric,” Indian J. Pure Appl. Math., 40, No. 3-4, 261–271 (1992).

    Google Scholar 

  18. U. Singh and S. Sonker, “Degree of approximation of function \( f\in {H}_p^{\left(\omega \right)} \) class in generalized Hölder metric by matrix means,” Math. Model. Sci. Comput., 283, 1–10 (2012).

    Google Scholar 

  19. L. Leindler, A. Meir, and V. Totik, “On approximations in Lipschitz norms,” Acta Math. Hung., 45, No. 3-4, 441–443 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  20. S. A. Telyakovskii, “On the rate of approximation of functions in Lipschitz norms,” Tr. Inst. Mat. Ural Otdel. Ros. Akad. Nauk, 16, No. 4, 297–299 (2010).

    Google Scholar 

  21. M. Gorenska, M. Lesniewicz, and L. Rempulska, “Strong approximation of functions in Hölder spaces,” Acta Sci. Math. (Szeged), 58, 233–241 (1993).

    MathSciNet  MATH  Google Scholar 

  22. R. A. Lasuriya, “Estimates for a group of deviations in generalized Hölder metric,” Ukr. Mat. Zh., 53, No. 9, 1210–1217 (2001); English translation: Ukr. Math. J., 53, No. 9, 1453–1463 (2001).

  23. B. Szal, “On the rate of strong summability by matrix means in the generalized Hölder metric,” J. Inequal. Pure Appl. Math., 9, No. 1, 1–27 (2008).

    MathSciNet  MATH  Google Scholar 

  24. A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2002).

    MATH  Google Scholar 

  25. N. L. Pachulia, “On the strong summability of Fourier series,” in: Problems of Summation of Simple and Multiple Series [in Russian], Preprint 87.40, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987).

  26. V. A. Rodin, “BMO-strong means of Fourier series,” Funkts. Anal. Prilozhen., 23, Issue 2, 73–74 (1989).

    MathSciNet  MATH  Google Scholar 

  27. M. F. Timan, Approximation and Properties of Periodic Functions [in Russian], Naukova Dumka, Kiev (2009).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 8, pp. 1056–1067, August, 2016.

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Lasuriya, R.A. Groups of Deviations of the Fourier Series in Generalized Hölder Spaces. Ukr Math J 68, 1208–1221 (2017). https://doi.org/10.1007/s11253-017-1288-8

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  • DOI: https://doi.org/10.1007/s11253-017-1288-8

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