Some Fixed Point Theorems For Nonlinear Contractions

In this paper,we discussed kinds of fixed point theorems for nonlinear contraction mappings in dislocated quasi-metric,fuzzy metric spaces and generalized fuzzy metric spaces.The main works are as follows.1.We show that a w-distance or a mw-distance in quasi-metric spaces can induce a dislocated quasi-metric.Then,we establish some fixed point theorems in dislocated quasi-metric spaces,which involve functions of Jachymski type.These results improve two recent results of Alegre et al.Some examples are also given to support our result.2.In complete Kaleva-Seikkala type fuzzy metric spaces,fixed point theorems for Boyd-Wong’s type,Alber-Guerre Delabriere’s type and Meir-Keeler’s type nonlinear con-tractions are established.These results improve and enrich some recent results of Xiao et al.As applications of our results,fixed point theorems for nonlinear contractions in ordinary metric spaces are obtained.3.We introduce a concept of generalized fuzzy metric spaces(in the sense of Kaleva and Seikkala)and establish some fixed point theorems for nonlinear contractions of Boyd-Wong’s type,Meir-Keeler’s type and(φ,φ)-weakly contractive type in generalized fuzzy metric spaces.Our results generalize and extend several known results in generalized metric spaces.