Tauberian conditions under which convergence follows from the weighted mean summability and its statistical extension for sequences of fuzzy number

Abstract

UDC 517.5 Let be a sequence of nonnegative numbers such that andLet be a sequence of fuzzy numbers.The weighted mean of is defined byIt is known that the existence of the limit implies that of For the the existence of the limit - we require the boundedness of in addition to the existence of the limit 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 follows from that of or - These Tauberian conditions are satisfied if satisfies the two-sided condition of Hardy type relative to