Common Fixed Point Theorems For Contractive Mappings Of Integral Type And Their Applications In A System Of Functional Equations

In this paper,the main idea is to combine the ideas of Branciari and Nadler,by increasing the terms in the maximum at the right end of the contractive inequality of integral type and the terms of the function of the inequality,several common fixed point theorems are proposed.Firstly,this paper introduces the introduction and preparatory knowledge.The introduction mainly introduces the work of scholars at home and abroad on the contractive mappings of integral type.The preparatory knowledge mainly introduces the basic knowledge,symbols,definitions and lemmas used in this paper.Secondly,the main theorems of this paper are given,the common fixed point theorems for contractive mappings of four single valued integral type and four set-valued integral type are introduced,and the proving processes are given,the proving process of individual theorems are similar to that of other theorems proving processes,so they are omitted.The Theorems 2.1-2.4 mainly combine with the idea of Branciari,by increasing the terms in the maximum at the right end of the contractive inequality of integral type and the terms of the function of the inequality,four common fixed point theorems for contractive mappings of integral type are obtained.Theorems 2.5-2.8 mainly combine Nadler's idea,transform the constant coefficients of the contractive inequality into functions,and establishe four common fixed point theorems for contractive mappings of set-valued integral type.Thirdly,three examples are constructed to show how the theorems are generalize or different from other fixed point theorems.Example 3.1 shows that Theorems 2.1 and 2.2 generalize the results of Branciari^[1]and Rhoades^[2]and are different from that of Liu^[3].Example 3.2 shows that Theorem 2.4 is different from that of Liu^[3].Example 3.3 shows that Theorems 2.5 and 2.6 are different from that of Ciric[8].Finally,the applications of the common fixed point theorems for contractive mapping of single valued integral type in a system of functional equations are given to seek the existence and uniqueness of solution of the system of functional equations.