A reduction principle for obtaining Tauberian theorems for statistical convergence in metric spaces
Terán, Pedro
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 295-299 / Harvested from Project Euclid
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We show a general method to translate Tauberian theorems for summability methods in $\mathbb R$ into Tauberian theorems for the corresponding forms of statistical convergence in metric spaces. The main tools (distance functions and the Hausdorff metric) come from set-valued analysis.
Publié le : 2005-04-14
Classification:  Statistical convergence,  Tauberian theorem,  summability,  distance function,  40E05,  40A05,  60D05 
@article{1117805090,
     author = {Ter\'an, Pedro},
     title = {A reduction principle for obtaining Tauberian theorems for statistical convergence in metric spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 295-299},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1117805090}
}

Terán, Pedro. A reduction principle for obtaining Tauberian theorems for statistical convergence in metric spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  295-299. http://gdmltest.u-ga.fr/item/1117805090/