Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters

  • Bogdan Szal University of Zielona Gora
  • Wlodzimierz Lenski University of Zielona Gora
Keywords: Rate of approximation, summability of Fourier series

Abstract

We extend and generalize the results of Xh. Z. Krasniqi [Acta Comment. Univ.
Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu.
Math. 13 (2009), 11-24], [Proc. Estonian Acad. Sci. 2018, 67, 1, 50--60] as
well the jont paper with M. Kubiak [Journal of Inequalities and Applications
(2018) 2018:92]. We consider the modified conjugate function  $\widetilde{f}%
_{r}$ for $2\pi /\rho $--periodic function $f$ . Moreover, the measure of
approximations depends on \textbf{\ }$\mathbf{\rho }$\textbf{ - }differences
of the entries of matrices defined the method of summability.

References

bibitem{XK} Xh. Z. Krasniqi, Slight extensions of some theorems on the rate

of pointwise approximation of functions from some subclasses of $L^{p}$,

Acta Comment. Univ. Tartu. Math. 17 (2013), 89-101.

bibitem{KLWBSZ4} M. Kubiak, W. Lenski and B. Szal, Pointwise approximation

of functions by matrix operators of their Fourier series with $r$-

differences of the entries, Journal of Inequalities and Applications (2018)

:92 .

bibitem{LWBSZ2} W. Lenski and B. Szal, Approximation of functions belonging

to the class $L^{p}(omega )$ by linear operators, Acta Comment. Univ.

Tartu. Math., 13 (2009), 11-24.

bibitem{LWBSZ3} W. Lenski and B. Szal, Pointwise approximation of modified

conjugate functions by matrix operators of their Fourier series, Proc.

Estonian Acad. Sci. 2018, 67, 1, 50--60.

bibitem{BSZal} B. Szal, A new class of numerical sequences and its

applications to uniform convergence of sine series, Math. Nachr., 284

-15(2011), 1985-2002.

bibitem{BSZal2} B. Szal, On $L$-convergence of trigonometric series, J.

Math. Anal. Appl., 373 (2011) 449--463.

bibitem{Z} A. Zygmund, Trigonometric series, Cambridge, 2002.

Published
2020-06-25
How to Cite
Szal, B., & Lenski, W. (2020). Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters. Tamkang Journal of Mathematics, 51(2), 145-159. https://doi.org/10.5556/j.tkjm.51.2020.3080
Section
Papers