Research On Several Kind Of Random Operator Problems

Some random fixed point problems base on some classical fixed point problems,they are a part of generalizations of the traditional fixed point. At present, the random fixed point theorems have been widely used in stochastic differential equations and stochastic integral equation. Some random fixed point theorems play an important role in stochastic differential equation and stochastic integral equation.In complete separable Banach spaces and complete separable metric spaces, this thesis discusse existence of fixed points random semi-closed 1-set-contractive operator, the random mapping sequence, random mixed monotone operators of random fixed points of random set-valued mappings sequence. The results show that the conditions in the existing of literature. This thesises also eablish a new definitions,improve and extend the existing literature results.This thesis includes four chapters:In chapter one, a brief introduced the research background and research work of my research are given. This chapter also states the relevant definitions and lemma of this article required.In chapter two, we discuss the solvability of the random semi-closed 1-setcontractive operator equation A(?, x)(28)?x in complete real separable Banach space,respectively, some new boundary conditions base on the condition of convex and concave function. Finally, this results prove the solution to the equation A(?, x)(28)?x and the fixed points existence of random semi-closed 1-set-contractive operator.In chapter three, we discuss the random couple mapping and random couple coincidence point and random couple fixed point theorems in a complete separable partially order metric space. And studied under the condition of weak compression,quadruple random mapping of quadruple random fixed point theorem. Results generalize the results in the existing literature, and the application of the theorem is given.In chapter four, we introduce more general random multivalued contractive mappings, and we establish the existence and uniqueness of random common fixedpoints for these random multivalued contractive mappings with weak compatibility.Our results extend, improve and unify the corresponding results and single value results in the literatures.