Study On Fixed Point Problems Of Some New F-Contraction Mappings

As one of the most important tools in Mathematical Science,the theory of fixed points plays an important role in the study of mathematics.Due to the complexity of mathematical problems,we have to add some mappings,parameters and some other conditions,this has aroused our interests in the study of fixed points.In this paper,we study mainly the existence of fixed points after adding some new mappings.In this paper,we study the fixed point problem of several new types F-contractive mappings in complete metric spaces.Firstly,the generalized F-contraction of the Ciric-type given by ?zlem et al is extended,we study the fixed point problem of the double contractive mappings in complete metric spaces and introduce a single-valued mapping g on the foundation of the original notion,we define a new Ciric-type F-contractive mapping with respect to g,at the same time,by means of generalized comparison function,we study the existence of fixed point of Ciric-type F-contractive mapping with respect to g.Finally,we obtain T and g have the same fixed point under certain conditions.Secondly,we find that the single-valued mappings can be extended to set-valued mappings,that is,a Ciric-type F-contractive mappings with respect to g is extended to the Ciric-type generalized set-valued F-contractive mapping with respect to g.By using Hausdorff metrics,some relatively weak conditions are added,we study the existence of the fixed point of the Ciric-type generalized set-valued F-contractive mappingwith respect to g,the results of the existence of common fixed points for T and g under certain condition are also obtained.In succession,we focus on the FL--contraction mapping studied by Gulhan et al.with bold imagination we add the single value mapping h,we defined a new FL--contraction mapping with respect to h,some analytic properties of the function are added,and two parameters ? and L are introduced,we study the new fixed point problem of FL--contraction mapping with respect to h,the results of the existence of common fixed points for T and h under certain conditions are also presented.Finally,inspired by authors Gulhan et al.,we continue to study the papers of fixed point problems with parameters,based on the paper of Monica et al.which study the fixed point problem of RH-class F-contractive mapping with five parameters,we continue to add a single valued mapping g,change the quantitative relationship between the five parameters and increase the analytical properties of the function,we get the results of the existence of common fixed points of T and g.Four kinds of fixed point problems of the new type of F-contractive mappings with respect to single-valued mapping g are studied in this paper,which extended the previous results of the single mapping to the double mappings,at the same time,the previous study of the single-valued mapping fixed point problem is extended to the set-valued mapping fixed point problem.It provides good foundation for the future study of the double mappings,and broadens the ideas and methods for the study of more complicated mapping fixed point problems.