  In this paper, we introduce the notion of $\alpha$--contractive mapping of
Meir--Keeler type in complete metric spaces and prove new theorems which assure
the existence, uniqueness and iterative approximation of the fixed point for
this type of contraction. The presented theorems extend, generalize and improve
several existing results in literature. To validate our results, we establish
the existence and uniqueness of solution to a class of third order two point
boundary value problems.
