Kambak, ÇağlaÇanak, İbrahim2024-07-122024-07-122019Kambak, Ç. ve Çanak, İ. (2019). Necessary and sufficient tauberian conditions under which convergence follows from Ar,? summability. International Conference of Mathematical Sciences (ICMS 2019). s. 66.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2118We say that (xmn) is (A r,? , 1, 1) summable to l if the sequence (? r,? mn(x)) has a finite limit l. It is known that if limm,n?? xmn = l and (xmn) is bounded, then the limit limm,n?? ? r,? mn(x) = l exists. But the inverse of this implication is not true in general. Our aim is to obtain necessary and sufficient conditions for (A r,? , 1, 1) summability method under which the inverse of this implication holds. Following Tauberian theorems for (A r,? , 1, 1) summability method, we also define A r and A ? transformations of double sequences and obtain Tauberian theorems for the (A r,? , 1, 0) and (A r,? , 0, 1) summabillity methods.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessPringsheim’s convergenceSlow decrease and slow oscillation in different sensesTauberian conditions and theoremsArticle6666