Common fixed point theorems for six mappings with some weaker conditions in 2-metric spaces

In this paper, we prove unique common fixed-point theorems for six mappings (two set-valued and four single-valued mappings) without assuming compatibility and continuity of any mapping on noncomplete 2-metric spaces. To prove these theorems, we introduce a noncompatible condition, that is, weak commutativity of type (Kh) in a 2-metric space. We show that completeness of the whole space is not necessary for the existence and uniqueness of common fixed point. Also, we prove common fixed point theorems for two self mappings and two sequences set-valued mappings by the same weaker conditions. Our results improve, extend and generalize the corresponding results given by many authors.