Research On Some Fixed Points Of Nonlinear Operators In Probabilistic Metric Analysis

In probabilistic metric analysis, the distance between two elements is measured by a distribution function, and an ordinary metric space can be viewed as a special case of a probabilistic metric analysis. So the study of nonlinear operators in probablistic metric analysis is significant. In this paper, the problems of new fixed points for nonlinear operators are investigated. It is divided into the following four sections in whole paper.In chapter one, the historical backgrounds and developing current situation of operator theory in probabilistic analysis are introduced and the basic knowledges are given.In chapter two, by means of using topological degree's theorems, some theorems are established in. Z-P-S space, studying the problems of the existence of solution of a class of nonlinear operator equation; furthermore, some theorems are established in Z-P-S space, which are based on the weaker Menger probabilisticâ–³-inner product space, continuously studying the problems of existence of its solution,and some new results are obtained.In chapter third, the contractive-type related concepts of Co probabilistic semigroups ar-e introduced to Menger PN-space spaces, these operators are not need of any compact,convex-concave,continuous properties and the cone is not being added to any additional conditions, which are abtained that some theorems of new common fixed points of the existence and uniquence of two classes of mixed monotone operators in Menger PN-space, which are based on the theorems of the cone.In chapter four, making full of the contractive concepts of C0 generating spaces of quasi-metric spaces semigroups, it is studying that the existence and uniquence of the new fixed points of a class of two binary operators in generating spaces of quasi-metric family. Moreover, two binary operators is not being added to any additional conditions that are compact,convex-concave,mixed monotone% continuous properties and any theorems of the cone,so that some new results are abtained. Finally, these results are applied to Menger PN-space spaces, continuously studying the problems of its new fixed points.