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Some properties of cosine series with coefficients from class of general monotone sequences order \(r\). (English) Zbl 1474.42016

Summary: The coefficient of sine series from general monotone class has been generalized by B. Szal [Math. Nachr. 284, No. 14–15, 1985–2002 (2011; Zbl 1230.40004)] to the new class which is called class of general monotone order \(r\). This coefficient class is more general than class of general monotone introduced by S. Tikhonov [J. Approx. Theory 153, No. 1, 19–39 (2008; Zbl 1215.42002)]. By special case, we study properties of cosine series with coefficient of sine series from the class of general monotone order \(r\).

MSC:

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
40A30 Convergence and divergence of series and sequences of functions
46A45 Sequence spaces (including Köthe sequence spaces)
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References:

[1] A. ZYGMUND, Trigonometric Series, Vol I, II, Second ed, Cambridge Univ. Press, 1959. · Zbl 0085.05601
[2] B. SZAL, A new class of numerical sequences and its applications to uniform convergence of sine series, arXiv: 0905.1294v1[math.CA], 8 May 2009. · Zbl 1250.40001
[3] M. A. IMRON, On Uniform Convergence of Sine and Cosine Series Under Generalized Difference Sequence of p-Supremum Bounded Variation Sequences, Int. Journal of Math. Analysis, Vol. 10, no. 6 (2016), pp. 245 - 256.
[4] M. A. IMRON, The Error Calculation of Sine Series Approximation with Coefficient from Class of General Monotone Orderr, AIP Conference Proceedings, Volume 2021 (060022), 2018.
[5] S. TIKHONOV, Best approximation and moduli of Smoothness computation and Equivalence Theorems, Journal of Approximation Theory, 153 (19-39), 2008. · Zbl 1215.42002
[6] T. W. CHAUNDY and A. E. JOLLIFE, The Uniform Convergence of certain class trigonometric series, Proc. London, Soc. 15, (1916) pp. 214-116 · JFM 46.0455.03
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