Fixed Point Theorems For Pairs Of Contractive Mappings Of Integral Type And Generalized Multivalued(F,?_?) And (F,?_?~m) Contractive Mappings And Applications

One of the issues that has received extensive attention in the field of nonlinear analysis is fixed point theory.Fixed point theory is widely applied in lots of significant fields such as functional equations,integral equations,differential equations and operational research.Large numbers of experts and scholars began to study mappings that satisfy different contractive conditions,and obtained many important results of fixed points and common fixed points.Inspired by Branciari's integral contractive type and Wardowski's F contractive type,the main content of this paper is divided into the following three parts:The first part is introduction.It mainly expounds the research background and research status of fixed point theorems and common fixed point theorems for contractive mappings of integral type,single-valued F contractive mappings and multivalued F contractive mappings in complete metric spaces.The second part proposes common fixed point theorems for pairs of weakly compatible mappings satisfying two different types of integral contractive conditions.Their contractive types are as follows:(?),(?),and by giving a valid,real-valued example,we prove that the results of this paper have developed the related results of Branciari,Liu et al,Vijayaraju et al and Kumar et al.Meanwhile,Theorem 1.1 and 1.2 are applied to verify the existence and uniqueness of the common solution of functional equations arising in dynamic programming,respectively.The third part mainly discusses the existence of fixed points of generalized multivalued(F,?_?) contractive mapping and generalized multivalued(F,?_?~m) contractive mapping in complete metric space.Their contractive types are as follows:(?),(?)A nontrivial example is given to verify that the results obtained in this paper extend the resultsof Nader,Altun et al and Olgun et al in complete metric spaces.In a word,this paper weakens or changes of the requirements of mappings and the contractive conditions of integral type in the existing literature,introduces two new concepts of generalized mutivalued(F,?_?) contractive mappings and generalized mutivalued(F,?_?~m)contractive mappings,and obtains some common fixed point theorems and fixed point theorems in complete metric spaces,respectively.The theorems of this paper are further supplements,refinements,and improvements to some well-known theorems.