Topological Transversality Of Random Operator

Random nonlinear operator theory is becoming more and more important intergradientof random nonlinear functional analysis. It has much closed relation to the other math-ematical branches. Especially, it plays an essential role in establishing the existence anduniqueness of the solutions of several kinds of random equations. There are many methodsto study random fixed point of stochastic nonlinear operator ,and it is particularly noteworthyto randomly analog fixed point of determined operator .This paper ,firstly introduces a number of well-known fixed point theorem and simpleapplication of the random fixed point theorem,then random analog topological transversalityof determined operator and gives application about the existence of the solutions of equation. The material in this book is presented in four chapters.the first chapter introduces the backgrounds and current situation of random fixed-pointtheories and The main research of this thesis.The second chapter is the prepareing knowledge. And it introduces the prepareingknowledge From the three facets of the normed space, set-valued mapping, random operator.the third chapter simply introduces Banach,Schauder,Krasnoselskii fixed point the-orem, and their provation .at the same time it gives two applications of random fixed pointtheorems.The last chapter studies topology Transversality of random operator in Banach spaceswhich is acquired according to analogy of topology Transversality in literature[1],In theprocess of random analog main difficulty lies in the establishment of the fixed points canbe measured, therefore, in order to technical difficulty, we are assuming that space is aseparable Banach space and Random operator is compact random operator and using thefixed point theories of the third chapter as well as some knowledge to solve the difficulty.Subsequently, we introduce simple application of topology Transversality of randomoperator.