Abstract
We discuss the relations between weighted mean methods and ordinary convergence for double sequences. In particular, we study Tauberian theorems also for methods not being products of the related one-dimensional summability methods. For the special case of theC 1,1-method, the results contain a classical Tauberian theorem by Knopp [9] as special case and generalize theorems given by Móricz [16] thereby showing that one of his Tauberian conditions can be weakened.
Abstract
Обсуздаутся соотнощения мезду определяемои методами вэвещенных средних и обычнои сходимостяу двоиных последователяностеи. В частности, иэучаутся тауберовы теоремы для методов, не являушихся проиэведением соответствууших одномерных методов суммирования. Реэулятаты обобшаут теоремы Ф. Морица дляC 1,1 -метода эа счет того, что одно иэ его тауберовых условии мозно ослабитя.
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Stadtmüller, U., Щтадтмуллер, У. Tauberian theorems for weighted means of double sequences. Anal Math 25, 57–68 (1999). https://doi.org/10.1007/BF02908426
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DOI: https://doi.org/10.1007/BF02908426