Necessary and sufficient conditions under which convergence follows from summability by weighted means
2001 ◽
Vol 27
(7)
◽
pp. 399-406
◽
Keyword(s):
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.
2004 ◽
Vol 41
(4)
◽
pp. 391-403
◽
2018 ◽
Vol 37
(4)
◽
pp. 9
2004 ◽
Vol 2004
(65)
◽
pp. 3499-3511
◽
2013 ◽
Vol 444-445
◽
pp. 621-624
2020 ◽
Vol 13
(5)
◽
pp. 1088-1096
2019 ◽
Vol 11
(2)
◽
pp. 251-263