Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences
Articles > Article · 2024
Authors: Ümit Totur, İbrahim ÇANAK
Ukrainian Mathematical Journal, Journal Indexed in SCI Expanded, International, WoS, 2024, vol 75, pp 1453-1472
DOI: 10.1007/s11253-024-02272-4
Summary
Let p = (pj) and q = (qk) be real sequences of nonnegative numbers with the property that Pm=∑j=0mpj≠0andQm=∑k=0nqk≠0forallmandn. Also let (Pm) and (Qn) be regularly varying positive indices. Assume that (umn) is a double sequence of complex (real) numbers, which is (N¯, p, q; α, β)-summable and has a finite limit, where (α, β) = (1, 1), (1, 0), or (0, 1). We present some conditions imposed on the weights under which (umn) converges in Pringsheim’s sense. These results generalize and extend the results obtained by the authors in [Comput. Math. Appl., 62, No. 6, 2609–2615 (2011)].