Geodesic
Necessary and sufficient Tauberian conditions under which convergence follows from summability $A^{r, p}$
Problemy analiza, Tome 10 (2021) no. 2, pp. 44-53

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In this paper, we introduce the summability method $A^{r, p}$ and obtain necessary and sufficient Tauberian conditions under which the ordinary convergence of a sequence follows from its summability $A^{r, p}$. The main results are new Tauberian theorems for the summability method $A^{r, p}$, which are generalizations of the corresponding Tauberian theorems for the summability method $A^r$ introduced by Başar.
Keywords: summability by $A^{r, p}$ method, slow oscillation, slow decrease, Tauberian condition. 
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     author = {\c{C}. Kambak and \.I. \c{C}anak},
     title = {Necessary and sufficient {Tauberian} conditions under which convergence follows from summability $A^{r, p}$},
     journal = {Problemy analiza},
     pages = {44--53},
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     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_2_a3/}
}
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Ç. Kambak; İ. Çanak. Necessary and sufficient Tauberian conditions under which convergence follows from summability $A^{r, p}$. Problemy analiza, Tome 10 (2021) no. 2, pp. 44-53. http://geodesic.mathdoc.fr/item/PA_2021_10_2_a3/