A Tauberian theorem for the weighted mean method of improper integrals of fuzzy-number-valued functions

Let 0 not equal p(x) be a nondecreasing real valued function on [0,infinity) such that p(0) = 0 and [GRAPHIC] Given a fuzzy-number-valued continuous function f (x) on [0,infinity), we define [GRAPHIC] It is known that the limit lim(x ->infinity) s(x) = mu exists, then the limit lim(x ->infinity) sigma(x) = mu also exists. But the converse of this implication need not be satisfied in general. In this paper, our goal is to find a condition under which the existence of lim(x ->infinity) sigma(x) = mu follows from that of lim(x ->infinity) s( x) = mu. As special cases, we obtain some Tauberian conditions of slowly decreasing type and Landau type for the Cesaro summability method of improper integrals of fuzzy-number-valued functions.