APPROXIMATION OF PERIODIC FUNCTIONS BY SUB-MATRIX MEANS OF THEIR FOURIER SERIES

Year 2020, Volume: 10 Issue: 1, 279 - 287, 01.01.2020

X. Z. Krasniqi

Abstract

Some results on approximation of periodic functions are extended in two directions: Improving the degree of approximation of periodic functions by sub-matrix means of its Fourier series and such degree is applicable for a wider class of summbility matrices in the sense of their entries in which class of sequences belongs to.

Keywords

Fourier series , degree of approximation , periodic functions , non-decreasing sequences , Cesaro submethod.

References

• Srivastava, Shailesh Kumar; Singh, Uaday, (2014), Trigonometric approximation of periodic functions belonging to Lip(ω(t), p)-class. J. Comput. Appl. Math. 270, 223–230.
• Zhang, Renjiang, (2015), A note on the trigonometric approximation of Lip(ω(t), p)-class. Appl. Math. Comput. 269, 129–132.
• Mishra, Vishnu Narayan; Mishra, Lakshmi Narayan, (2012), Trigonometric approximation of signals (functions) in Lp-norm. Int. J. Contemp. Math. Sci. 7, no. 17-20, 909–918.
• Leindler, L, (2004), On the degree of approximation of continuous functions. Acta Math. Hungar. 104, no. 1-2, 105–113.
• Armitage, David H.; Maddox, Ivor J, (1989), A new type of Ces`aro mean. Analysis 9, no. 1-2, 195–206.
• Osikiewicz, Jeffrey A, (2000), Equivalence results for Ces`aro submethods. Analysis (Munich) 20, no. 1, 35–43.
• Mittal, M. L.; Singh, Mradul Veer, (2016), Applications of Ces`aro submethod to trigonometric ap- proximation of signals (functions) belonging to class Lip(α, p) in Lp-norm. J. Math., Art. ID 9048671, 7 pp.
• Mittal, M. L.; Singh, Mradul Veer, (2014), Approximation of signals (functions) by trigonometric polynomials in Lp-norm. Int. J. Math. Math. Sci., Art. ID 267383, 6 pp.
• Mohapatra, N. Ram and Szal, Bogdan, On trigonometric approximation of functions in the Lp-norm, https://arxiv.org/pdf/1205.5869.pdf.