Some New Random Fixed Point Theorems For Several Classes Of Random Operators

Random nonlinear operator theory is becoming more and more important intergradient of random nonlinear functional analysis.It has much closed relation to the other math-ematical branches.The study of random fixed points which is considered as a central topic, in which some well-known sochastic fixed point theorems were well proved. There are many methods to study random fixed points of stochastic nonlinear operators. In this thesis, utilizing random fixed point index theory and iteration method, random fixed point theorems of different classes of random nonlinear operators and the equation solution existence problem for one type random multi-valved mapping are studied; and we obtain some new random fixed point theorems by randomized promoting some well-known theorems and results. There are three chapters in this thesis.Chapter Ⅰ,the backgrounds and current situation of random fixed point theories are introduced and knowledge about random nonlinear operators is given.Chapter Ⅱ,in Banach spaces,utilizing the random fixed point index and some important results,we obtain several new results and extend random fixed point theorems of random expansion and compression for two classes of random functional.Chapter Ⅲ,first of all,some random fixed point theorems about a class of nonexpansive and quasi-nonexpansive random operators are discussed in cone norm space;secondly,the equation solution existence problem about a class of random set-valued semi-closed1-set contractive operator is studied by utilizng the characters of concave,convex and monotone functions; finally,with random Mann and random Ishikawa iteration schemes,some random fixed point theorems about random weakly contractive maps are proved.