Common Fixed Point And Coupling Coincidence Point Theorems Of Several Types Of Contraction Mappings

Fixed point theory is an important tool for studying nonlinear functional analysis problems,and has a far-reaching influence in the field of mathematics.This article focuses on soft metric space,S-symmetric space,b-metric space and quasi-metric space.Common fixed point and coupled fixed point theorems.The full text is divided into five chapters.Chapter 2 first introduces the definition of mixed monotonic mapping and soft metric.Secondly,it proves a fixed point theorem on soft metric product space and a strongly coupled soft fixed point theorem for mixed monotonic single-valued mapping in soft metric space.Finally,the requirement that T is satisfied is that a is mixed mono tonic and T(Y × Y)?(α(Y)×α(Y)),the existence and uniqueness of the fixed point of the mapping T is obtained.And it is proved that the mapping S and the mapping a satisfying the α-mixed monotonicity The strong coupling common soft fixed point theorem.In Chapter 3,based on the complete S-symmetric space,we first discuss the strong coupling fixed point theorem of the mapping under certain compression conditions on the product space.Second,we discuss the strong coupling coincidence of the two mappings under the corresponding conditions.Point theorem.Finally,define two commutative mappings f:(?)Xr→X and g,which prove that the two mappings meet the corresponding The existence and uniqueness of the coincidence point of the r-tuple is strong when the condition is compressed.Chapter 4 defines the b-metric space and measurable function of random operators,and uses this as a background to discuss the existence and uniqueness of the fixed point of the mapping T containing the measurable choice ξ.Expansion,under certain conditions,the existence and uniqueness of the coincidence point of two mappings K and T is proved.Chapter 5 takes the quasi-metric space as the spatial framework,and gives the common fixed point theorems of two single-valued mappings,and further generalizes them to the common fixed point theorems of r-single-valued mappings.Chapter 6 is the summary and outlook.