Fixed Point Theorems In Probabilistic Metric Spaces And Applications

Firstly,this thesis study some new fixed point theorems of nonlinear operators under some new contraction conditions in probabilistic metric spaces;Secondly,ordered relationships are led to probabilistic metric spaces and we discuss some operators' random coupled coincidence point theorems in specific condition.What's more,contractive operator of probabilistic metric space is extended to the fuzzy metric spaces and cone b-metric spaces and obtained some corresponding fixed point theorems.This thesis is divided into four chapters.In the first chapter,background and history of development,the main problems and its significance and methods are introduced and we also give some basic concepts of probabilistic metric space.In the second chapter,the existence and uniqueness of multiple common fixed point theorems are studied under new contraction condition in probabilistic metric spaces.In the third chapter,the concept of ordered relationships is introduced in the probability metric space and the random coupled coincidence point theorem of two operators which satisfy the mixed g-monotone are further discussed.The fourth chapter,some conclusions are obtained in fuzzy metric space and the cone b-metric space and complete metric spaces,and an open question were answer about Rus raised in the literature [59].