This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.
@article{bwmeta1.element.doi-10_2478_s11533-008-0019-7, author = {\.Ibrahim \c Canak and \"Umit Totur}, title = {Tauberian theorems for Abel limitability method}, journal = {Open Mathematics}, volume = {6}, year = {2008}, pages = {301-306}, zbl = {1162.40003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0019-7} }
İbrahim Çanak; Ümit Totur. Tauberian theorems for Abel limitability method. Open Mathematics, Tome 6 (2008) pp. 301-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0019-7/
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