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

Abstract

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.

Mathematics Subject Classification (2010):

• 47H10
• 54H25
• 54E50
• 26A18

Keywords:

• Fixed point
• k-Meir-Keeler function
• closed graph function
• complete metric space
• k-graph pseudometric