Common Fixed Point Theorems Of Integral Type And Suzuki Type Contractive Mappings And Their Applications In Two Kinds Of Equations

Banach contraction principle is one of the basic theoretical achievements of fixed point theory.For more than a decade,scholars have been promoting it into many directions,like integral type contractions and F-contractions.This paper studys the integral type and Suzuki type contractive mappings,and proves several fixed point theorems of nonlinear integral type and Suzuki type contractive mappings in G-metric spaces.This paper consists of four parts.The first part is composed of introduction and fundamental knowledge.The introduction mainly introduces the development status of G-metric space,integral type and Suzuki type contractive mappings and important results obtained by scholars.The fundamental knowledge mainly introduces the symbols,definitions and lemmas in this paper.The second part is the main part of this paper,giving seven theorems and their proof processes.In the second chapter,on the basis of Branciari’s thought,four kinds of contractive mappings are obtained by adding and changing the terms in the Maximum M_i(x,y,z)at the right end of the inequality.And the four common fixed point theorems of different nonlinear integral contractive mappings are proved by exploring the conditions met by ψ and φ in the contractive mappings.For these four theorems,the proof processes of some theorems are given in this paper.The proof processes of similar theorems are omitted.The third chapter is inspired by Aggarwal’s and Esfahani’s ideas.The fixed point and common fixed point theorems of three Suzuki type contractions are obtained in complete G-metric spaces by redefining θ functions.And the existence and uniqueness of fixed point and common fixed point are proved.The third part is composed of the examples and applications.The fourth chapter constructs four examples.Example 4.1 and 4.2 illustrate that the four theorems in the second chapter generalize Shatanwi’s and Aydi’s theorems and are different from Shozib’s theorems.Example 4.3 and 4.4 are respectively the applications of the two theorems in the third chapter.In the fifth chapter,several applications of fixed point theorems of nonlinear integral type and Suzuki type contraction in functional equations and integral equations are given,respectively.And this article explores the applications of functional equations and integral equations arising in dynamic programming with the help of common fixed point theorems.It also illuminates the existence and uniqueness of solution to the two kinds of equations.The fourth part mainly includes the references involved in this paper,papers published during postgraduate study and acknowledgements.