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Tauberian Theorems for Weighted Means of Double Sequences

โœ Scribed by Chang-Pao Chen; Jui-Ming Hsu


Book ID
110228278
Publisher
Springer
Year
2000
Tongue
English
Weight
265 KB
Volume
26
Category
Article
ISSN
0133-3852

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๐Ÿ“œ SIMILAR VOLUMES


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We discuss the relations between power series methods, weighted mean methods, and ordinary convergence for double sequences. In particular, we study Tauberian theorems for methods being products of the related one-dimensional summability methods.

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Let (x jk : j, k = 0, 1, 2, . . .) be a double sequence of real or complex numbers, and set x jk for m, n = 0, 1, 2, . . . . We give necessary and sufficient conditions, under which st-lim ฯƒ mn = ฮพ implies st-lim x jk = ฮพ, where ฮพ is a finite number. These Tauberian conditions are one-sided when th