A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers

Let X and Y be two sequence spaces and A = (ank) be an infinite matrix. If for each x ∈ X the series An(x) = ∑∞ k=0 ankxk converges for each n and the sequence Ax = (Anx) ∈ Y we say that the matrix A maps X into Y . By (X,Y ) we denote the set of all matrices which map X into Y . Let c be the set of all convergent sequences. A matrix A is called regular if A ∈ (c, c) and limn→∞Anx = limk→∞ xk for all x ∈ c. The matrix representation of weighted mean method (N, p) is denoted by W = (wnk), where wnk is defined by wnk = pk Pn if k ≤ n and wnk = 0 otherwise. It is known that (N, p) summability method is regular, i. e, W ∈ (c, c)reg if and only if (1) holds.