Common fixed point theorems in L-fuzzy metric spaces

In this paper, at first we prove a common fixed point theorem in L-fuzzy metric space. Secondly, to introduce the concept of compatible mappings of type (P) in L-fuzzy metric space, which is equivalent to the concept of compatible and compatible mappings of type (A) under some appropriate conditions. In the sequel, we derive some relations between these mappings. Then, we prove a coincidence point theorem and a fixed point theorem for compatible mappings of type (P) in L-fuzzy metric space, for four mappings.