Fixed Point Theorems For Set-valued Mappings

Fixed point theorem is applied successfully in many fields,such as economic balance problems,algebraic equation,function equation,game theory,differential equation and so on,therefore,fixed point problems received wide attention by many scholars both at home and abroad.This paper proves that a Nadler type set contractive mapping has a fixed point in a complete metric-like space.This thesis consists of three chapters:The first chapter is introduction,we briefly introduce the developing course and related historical background of the fixed point theorem.This chapter also introduce the concept of lower semi-continuity from above functions and related theoretical results.In the second chapter,we introduce the concept of metric-like space,and prove that a set valued contractive mapping on a complete metric-like space has a fixed point by using lower –continuous from above condition.In the third chapter,we study the fixed point problem for a class of set valued mappings.We obtain a fixed point theorem for this set valued type mapping in a complete metric-like space.