On The Krasnoselskii- Type Fixed Point And Fixed-set Of Set-valuued Mapping

Fixed point theory has important applications in mathematics , physics, economics and so on. This paper is concernd with a special kind mappings- Krasnoselskii-type mappings.when one oprator is set-valued ,some fixed point theorems are established. The full text is divided into four chapters:Chapter I, Introduction: This chapter is mainly introduces the background and the research situation of the topics in our country and abroad.Chapter II, Type of set-valued mappings Krasnoselskii fixed point theorem: in this chapter,we use Shauder Fixed point theorem to obtain the fixed point of the operator A + B. Here, our work mainly displays in: Firstly, A is from a single value mapping to a set-valued mapping. Secondly, B is must not be a reversible mapping. In addition, we also get a invariant set of the operator A + B, Namely, there exits a set M makes (?)Chapter III, Fixed point theorem of set-valued mapping under non-compactness: in this chapter, by means of measures of noncompact, we finded a set N 0,then, we use Shauder Fixed point theorem to obtain the fixed point of the operator A + B under the set N 0. In addition,we also had the existence of the invariant sets of the operator A + B. Here, A is a set-valuedmapping, IB is not necessary reversible.While ,the previous conclusions on Krasnoselskii fixed point theorem are greatly generalized. Chapter IV, The development and outlook of the paper.