We obtain a common fixed point theorem for a sequence of fuzzy mappings, satisfying
a contractive definition more general than that of Lee, Lee, Cho and Kim [2].Let (X,d) be a complete linear metric space. A fuzzy set A in X is a function from X into
[0,1]. If x∈X, the function value A(x) is called the grade of membership of X in A. The α-level
set of A, Aα:={x:A(x)≥α, if α∈(0,1]}, and A0:={x:A(x)>0}¯. W(X) denotes the
collection of all the fuzzy sets A in X such that Aα is compact and convex for each α∈[0,1]
and supx∈XA(x)=1. For A,B∈W(X), A⊂B means A(x)≤B(x) for each x∈X. For
A,B∈W(X), α∈[0,1], define
Pα(A,B)=infx∈Aα,y∈Bαd(x,y), P(A,B)=supαPα(A,B), D(A,B)=supαdH(Aα,Bα),
where dH is the Hausdorff metric induced by the metric d. We notc that Pα is a nondecrcasing
function of α and D is a metric on W(X).Let X be an arbitrary set, Y any linear metric space. F is called a fuzzy mapping if F is a
mapping from the set X into W(Y).In earlier papers the author and Bruce Watson, [3] and [4], proved some fixed point theorems
for some mappings satisfying a very general contractive condition. In this paper we prove a fixed
point theorem for a sequence of fuzzy mappings satisfying a special case of this general contractive
condition. We shall first prove the theorem, and then demonstrate that our definition is more
general than that appearing in [2].Let D denote the closure of the range of d. We shall be concerned with a function Q, defined
on d and satisfying the following conditions:
(a) 0<Q(s)<s for each s∈D\{0} and Q(0)=0(b) Q is nondecreasing on D, and(c) g(s):=s/(s−Q(s)) is nonincreasing on D\{0}
LEMMA 1. [1] Let (X,d) be a complete linear metric space, F a fuzzy mapping from X
into W(X) and x0∈X. Then there exists an x1∈X such that {x1}⊂F(x0).
