The Fixed Point Theorem On Rectangular B-metric Space

The research of fixed-point theorem has a long history.As early as 20th century,famous mathematicians had studied it.This field of research is relatively wide,and it has been expanding from the initial metric space.Moreover,there are many functions of different compression in the same space which can be studied.It has broad research prospects.Firstly,this paper introduced the history and basic concepts of fixed point theory.Then we introduced the definition of the generalized type Suzuki-Berinde ? contractive mapping in the second part of paper.We created a new auxiliary function,and proved the existence and uniqueness of the fixed point for such kind of generalized type Suzuki-Berinde ? contractive mapping.We generalized the similar result of fixed point theorem in the setting of metric space,and obtained a new fixed point theorem of rectangular b-metric space.The third part of paper,we introduced the definition of generalized type?-? Suzuki contractive mapping in the setting of rectangular b-metric spaces.Then we proved the existence and uniqueness of the fixed point for this mapping in the setting of rectangular b-metric spaces.And we also introduced a new lemma to prove the relationship between generalized type ?-? Suzuki contractive mapping and Kannan contractive mapping.That is a new generalization for such kind of fixed point theorem.The last part of paper,we created generalized triangular ?-admissible mapping by developing triangular?-admissible mapping.And proved the fixed point theorem of generalized triangular?-admissible mapping under certain conditions.