Some Fixed Point Theorems For Mappings Satisfying F?contractive Conditions Of Integral Type

Banach fixed point theorem is one of the most fundamental and famous results in fixed point theory,it developed the iterative ideas and provided the means for solving the existence and uniqueness of solution in many field.As the really generalization of Banach fixed point theorem,the fixed point theorem of mappings of integral type presented by Baranciari and the fixed point theorem of mappings satisfying F-contractive conditions presented by Wardowski get a lot of attention.Baranciari first presented the integral type of contractive mapping,and proved the existence of the fixed point of the mapping in complete metric space.However,Wardowski extended Banach`s result in a new way.Wardowski introduced the concept of F-contraction,and used the mapping F to prove the existence,uniquenss and iterative approximations of the fixed point of the mappings satisfying F-contractive conditions in complete metric space.On this foundation,this paper combines the thoughts of Baranciari and Wardowski,and respectively presents F-contractive mappings of integral type with respect to a mapping and a pair of mappings.For a mapping,this paper proves the existence,uniquenss and iterative approximations of the fixed point of the mapping in complete metric space with different conditions.In addition,this paper also researchs another type of a mapping satisfying F-contraction of integral type,and obtains corresponding result in order metric space.For a pair of mappings,this paper proves the existence and uniquenss of the common fixed point of the mappings in metric space and order metric space,respectively.Our results extend and improve some results in the literature.The composition of this paper is: the first part is introduction,which is to introduce the background,meaning and recent progress of contractive mappings,and give the forms of four new type of contractive mappings presented by this paper,also explain them research situation and corresponding examples briefly;in order to convenience the reading and comprehension for this paper,the second part is to define the symbols,the functions and the family of functions mentioned in this paper,and introduce the theoretical knowledge and two important lemmas related to this paper;the third part is the main contents of this paper,seven theorems about four new type of contractive mappings presented by this paper;the fourth part is four examples,this paper gives the specific forms of the functions and the coefficient in the theorems to understand and illustrate the results of this paper better.