Fixed point theorems for two new types of cyclic weakly contractive mappings in partially ordered Menger PM-spaces

In this paper, we introduce the concepts of cyclic weakly ( ψ , ϕ )-contractive mappings and cyclic weakly ( C , ψ , φ )-contractive mappings, and prove some fixed point theorems for such two types of mappings in complete partially ordered Menger PM-spaces. Some new results are obtained, which extend and generalize some fixed point results in metric and probabilistic metric spaces. Some examples are given to support our results.