We prove common fixed point theorems for weakly compatible mappings via an implicit relation in fuzzy metric spaces using property (E.A) and a common property (E.A). Our theorems extend theorems of [1, 3, 4, 6, 15, 16] and a corollary of [2].

In this paper, principally supplemented modules are defined as generalizations of lifting, principally lifting and supplemented modules. Several properties of these modules are proved. New characterizations of principally semiperfect rings are obtained using principally supplemented modules.

It is well-known that the nonconvex variational inequalities are equivalent to the fixed point problems. We use this equivalent formulation to suggest and analyze some three-step iterative methods for solving the non-convex variational inequalities. We prove the convergence of the three-step iterative methods under suitable weaker conditions. Several special cases are also discussed. Our method of proof is very simple.