We extend the results of Xh. Z. Krasniqi (Acta Comment. Univ. Tartu Math. 17:89–101, 2013) and the authors (Acta Comment. Univ. Tartu Math. 13:11–24, 2009; Proc. Est. Acad. Sci. 67:50–60, 2018) to the case when considered function is -periodic and the measure of approximation depends on r-differences of the entries of the considered matrices.
We introduce a new class of double sequences called DGM (p, α, β, γ, r), which is a generalization of a class considered by Duzinkiewicz and Szal (2018). We obtain a necessary condition for the uniform convergence of double sine series with coefficients belonging to this class.
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