Double Trigonometric Series and Zygmund Classes of Functions with Two Variables (communicated by Hüsein Bor)
نویسندگان
چکیده
In the present paper, we generalize Zygmund classes of functions with two variables defined by Móricz by means of modulus of continuity, and give the necessary and sufficient conditions for double sine, sine-cosine, cosinesine and double cosine series so that their sums belong to the generalized Zygmund classes. Some new results of Fülöp [1] and [2] on double trigonometric series are extended.
منابع مشابه
Best Approximation of Functions of Generalized Zygmund Class by Matrix-euler Summability Means of Fourier Series (communicated by Hüsein Bor)
The degree of approximation of a function f belonging to Lipschitz class by the Cesàro mean and f ∈ Hα by the Fejér means has been studied by Alexits [4] and Prössdorf [7] respectively. But till now no work seems to have been done to obtain best approximation of functions belonging to generalized Zygmund class, Z (w) r , (r ≥ 1) by product summability means of the form (∆.E1). Z (w) r class is ...
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