On the uniform convergence of sine, cosine and double sine-cosine series

• Autorzy: Krzysztof Duzinkiewicz
• Języki publikacji: EN

Abstrakty

EN

In this paper we define new classes of sequences GM(β,r) and DGM(α,β,γ,r). Using these classes we generalize and extend the P. Kórus results concerning the uniform convergence of sine, cosine and double sine-cosine series, respectively.

Słowa kluczowe

EN

sine series; cosine series; double sine-cosine series; uniform convergence; generalized monotonicity

Kategorie tematyczne

• 42B99: None of the above, but in this section
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2016
• Tom: 36
• Numer: 1
• Strony: 87-116

Daty

wydano

2016

otrzymano

2016-03-03

poprawiono

2016-04-03

Twórcy

autor

Krzysztof Duzinkiewicz

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góora, ul. Szafrana 4a, 65-516 Zielona Góra, Poland

Bibliografia

• [1] T.W. Chaundy and A.E. Jolliffe, The uniform convergence of certain class of trigonometrical series, Proc. London Math. Soc. 15 (1916), 214-216.
• [2] K. Duzinkiewicz and B. Szal, On the uniform convergence of double sine series, http://arxiv.org/pdf/1510.06273v1.pdf.
• [3] P. Kórus, Remarks on the uniform and L1-convergence of trigonometric series, Acta Math. Hungar. 128 (2010), 369-380. doi: 10.1007/s10474-010-9217-4
• [4] P. Kórus, On the uniform convergence of double sine series with generalized monotone coefficients, Periodica Math. Hungar. 63 (2011), 205-214. doi: 10.1007/s10998-011-8205-y
• [5] P. Kórus, Uniform convergence of double trigonometric series, Mathematica Bohemica 138 (3) (2013), 225-243.
• [6] 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.
• [7] B. Szal, On L-convergence of trigonometric series, J. Math. Anal. Appl. 373 (2011), 449-463. doi: 10.1016/j.jmaa.2010.08.003
• [8] D.S. Yu and S.P. Zhou, A generalization of monotonicity condition and applications, Acta Math. Hungar. 115 (2007), 247-267. doi: 10.1007/s10474-007-5253-0
• [9] S.P. Zhou, P. Zhou and D.S. Yu, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, Sci. China Math. 53 (7) (2010), 1853-1862. doi: 10.1007/s11425-010-3138-0
• [10] I.E. Žak and A.A. Šneider, Conditions for uniform convergence of double sine series, Izv. Vysš. Učebn. Zaved. Matematika 4 (1966) in Russian, 44-52.

Identyfikatory

DOI

10.7151/dmdico.1177