Necessary and sufficient conditions under which convergence follows from summability by weighted means
We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted mean methods and unify the results known in the literature for particular methods. Among others, the conditions in our theorems are easy conseq...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006688 |
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| Summary: | We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted mean methods and unify the results known in the literature for particular methods. Among others, the conditions in our theorems are easy consequences of the slowly decreasing condition for real numbers, or slowly
oscillating condition for complex numbers. Therefore, practically all classical (one-sided as well as two-sided) Tauberian conditions for weighted mean methods are corollaries of our two
main theorems. |
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| ISSN: | 0161-1712 1687-0425 |