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sine series; cosine series; double sine series; sine-cosine series; double cosine series; uniform convergence; regular convergence; general monotone sequence; general monotone double sequence; supremum bounded variation

References:

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[7] Móricz, F.: **Some remarks on the notion of regular convergence of multiple series**. Acta Math. Hung. 41 (1983), 161-168. DOI 10.1007/BF01994074 | MR 0704536

[8] Tikhonov, S.: **Trigonometric series with general monotone coefficients**. J. Math. Anal. Appl. 326 (2007), 721-735. DOI 10.1016/j.jmaa.2006.02.053 | MR 2277815 | Zbl 1141.42004

[9] Tikhonov, S.: **Best approximation and moduli of smoothness: Computation and equivalence theorems**. J. Approx. Theory 153 (2008), 19-39. DOI 10.1016/j.jat.2007.05.006 | MR 2432551 | Zbl 1215.42002

[10] Zhak, I. E., Shneider, A. A.: **Conditions for uniform convergence of double sine series**. Russian Izv. Vyssh. Uchebn. Zaved., Mat. 53 (1966), 44-52.

[11] Zhou, S. P., Zhou, P., Yu, D. S.: **Ultimate generalization to monotonicity for uniform convergence of trigonometric series**. Sci. China, Math. 53 (2010), 1853-1862. DOI 10.1007/s11425-010-3138-0 | MR 2665519 | Zbl 1211.42006