Tauberian conditions under which convergence follows from the weighted mean summability and its statistical extension for sequences of fuzzy number - Önder, Z.; Çanak, İ. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.5 Let (p_n) be a sequence of nonnegative numbers such that p_0>0 and P_n:=_k=0^np_k→∞asn→∞. Let (u_n) be a sequence of fuzzy numbers. The weighted mean of (u_n) is defined by t_n:=1P_n_k=0^np_k u_kforn =0,1,2,… . It is known that the existence of the limit u_n=μ_0 implies that of t_n=μ_0. For the the existence of the limit st-t_n=μ_0, we require the boundedness of (u_n) in addition to the existence of the limit u_n=μ_0. But, in general, the converse of this implication is not true. In this paper, we obtain Tauberian conditions, under which the existence of the limit u_n=μ_0 follows from that of t_n=μ_0 or st-t_n=μ_0. These Tauberian conditions are satisfied if (u_n) satisfies the two-sided condition of Hardy type relative to (P_n).