Necessary and Sufficient Conditions under Which Convergence Follows from Summability by Weighted Means
نویسندگان
چکیده
We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted meanmethods and unify the results known in the literature for particularmethods. 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. 2000 Mathematics Subject Classification. 40E05, 40C05.
منابع مشابه
Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense
After a brief summary of Tauberian conditions for ordinary sequences of numbers, we consider summability of double sequences of real or complex numbers by weighted meanmethods which are not necessarily products of related weighted mean methods in one variable. Our goal is to obtain Tauberian conditions under which convergence of a double sequence follows from its summability, where convergence ...
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