A tauberian condition under which convergence follows from the weighted mean summability of sequences of fuzzy number
Articles > Article · 2020
Authors: Zerrin Önder, İbrahim ÇANAK
Annals of the University of Craiova, Mathematics and Computer Science Series, Journal Indexed in SCI Expanded, International, Scopus, 2020, vol 47, pp 183-192
Summary
Let (un) be a sequence of fuzzy numbers and (pn) be a sequence of nonnegative numbers such that p0 > 0 and Pn:=Σnk=0pk→∞ as n→∞. The weighted mean of (un) is defined by tn:=1/PnΣnk=0pk uk for n = 0, 1, 2,... It is well known that convergence of (un) implies that of the sequence (tn) of its weighted means. However, the converse of this implication is not true in general. In this paper, we investigate under which conditions convergence of (un) follows from its weighted mean summability. We prove a Tauberian theorem including condition of slow decrease with respect to the weighted mean summability method for sequences of fuzzy numbers.