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Fixed point theory in mathematics, physics, and economic fields have a wide range of applications , this paper, a class of special set the value mapping Krasnoselskii type fixed point for discussion . Article is divided into four chapters : Chapter 1 Introduction : describes the subject of the proposed background , status , etc. ; Chapter II sets the value mapping Krasnoselskii type is not fixed point : In this chapter, we use E.zeidler fixed point theorem to obtain a fixed point of the operator AB here we work main theorem promotion, mainly in : a single-valued mapping extended to the set-valued mapping , B, here I ? B does not necessarily reversible mapping , we still I ? B irreversible case to the conclusion of an invariant set , exists M such that ( ? ) Chapter noncompact measure set - valued maps Krasnoselskii type fixed point : in this section , we use the non-compact measure , to find a collection of N 0 and N 0 is the basis of the use of E.zeidler fixed point theorem , resulting in a combination of fixed point operator AB , like we get the existence of the invariant set of the AB . a is a set-valued mapping , I ? B may not be reversible , this largely historical conclusions promotion. development and Prospect of the fourth chapter of the thesis .
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