A novel fixed point theorem for the k-Meir-Keeler function

Generalized Meir-Keeler functions are introduced that contain a class of weakly uniformly strict contraction maps. A theorem is proven that assures the existence of a fixed point for the closed k-Meir-Keeler functions and provides a con- structive method to find the points. An advantage of the method is that it is possible to show the existence of a fixed point for functions with domains that are neither complete nor closed.