On Uniform Convergence of Double Sine Series under Condition of p-Supremum Bounded Variation Double Sequences

Abstract

The classical theorem on the uniform convergence of sine series with monotone decreasing coefficients have been proved by Chaundy and Jollife in 1916. Recently, the monotone decreasing coefficiets has been generalized by classes of Mean Bounded variation Sequences, Supremum Bounded Variation Sequence and p-Supremum Bounded Variation Sequences. In two variables, class of Mean Bounded Variation Double Sequences and Supremum Bounded Variation Double Sequences were studied under the uniform convergence of double sine series. We shall generalize those results by defining class of p-Supremum Bounded Variation Double Sequences and study uniform convergence of double sine series. 2536 Moch Aruman Imron, Ch. Rini Indrati and Widodo Mathematics Subject Classification: 42A20, 42A32, 42B99

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