Discussion On Fixed Point Theorems Of Pata Type And (?)iri(?) Type

In this paper,we discussed kinds of fixed point theorems of Pata type and (?)iri(?) type in metric space,Kaleva-Seikkala’s type fuzzy metric space and dislocated quasi b-metric space.The main works are as follows1.A fixed point theorem of (?)iri(?)-Pata type is established in metric space.This result provides a complete solution to an open problem raised by Kadelburg and Radenovic.In particular,the main result extends several existing results.Moreover,an example is given in the support of our result2.We establish a new fixed point theorem for cyclic-contractive mapping of Pata type in metric space,and correct the errors in the process of proof by Alghamdi et al.The results obtained in this paper improve and unify some previous results3.We generalize the fixed point theorems for Banach-Pata type contraction and Kannan-Pata type contraction from metric spaces to Kaleva-Seikkala’s type fuzzy metric spaces.Moreover,two examples are given in the support of our results4.Fixed point theorems for several cyclic contractive mappings are established in dislocated quasi-b-metric spaces.The results obtained in this paper improve and unify some previous results in the existing literature.Moreover,several nontrivial examples are given to illustrate the superiority of the main results.As applications of our results,fixed point theorems for cyclic-contractive mapping in quasi-partial b-metric spaces are obtained.