b-距离空间中隐性压缩不动点定理

Fixed Point Theorems of Implicit Contractions in b-Metric Spaces

利用Suzuki给出的一个重要引理,在b-距离空间中建立了两类含有六元函数的隐性压缩不动点定理,其中一类结果将Berinde等人(2011)在距离空间建立的压缩不动点结果推广到b-距离空间.该文有关结果可以得到b-距离空间中Banach型,Kannan型,Chatterjea型不动点定理.特别地,Banach型的结果就是Dung等人(2016)在解决Jovanovi?等人(2010)提出的公开问题时得到的结果.另外一类结果将距离空间中Karapinar等人(2018)和四角距离空间中Aydi等人(2019)提出的两类新的不动点定理建立到b-距离空间,并统一了两种压缩条件.

By using Suzuki’s lemma,two classes of Fixed point theorems of implicit contraction containing six variable continuous functions are given in b-metric spaces.One of our results generalizes the theorems of Berinde et al.(2011)from metric spaces to b-metric spaces.As the corollaries,we obtain the Banach,Kannan and Chatterjea types of fixed point theorems in b-metric spaces.In particular,the corollary of Banach type is the result of Dung et al.(2016),which is an answer to the questions of Jovanovi?et al.(2010)The other one of our results unifies the contractive condition of two theorems in the setting of b-metric spaces,which were given by Karapinar et al.(2018)in metric spaces and Aydi et al.(2019)in rectangular metric spaces.