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

Authors

  • Bogdan Szal University of Zielona Gora
  • Wlodzimierz Lenski University of Zielona Gora

DOI:

https://doi.org/10.5556/j.tkjm.51.2020.3080

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

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.

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) 2018:92 .

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.

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.

B. Szal, A new class of numerical sequences and its applications to uniform convergence of sine series, Math. Nachr., 284 14-15(2011), 1985-2002.

B. Szal, On $L$-convergence of trigonometric series, J. Math. Anal. Appl., 373 (2011) 449--463.

A. Zygmund, Trigonometric series, Cambridge, 2002.

Additional Files

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

Issue

Section

Papers