Fixed Point Theorems For Contraction Mappings In Quasi-partial Metric Space

The paper mainly studies the fixed point theorems of several contractive type maps on quasi-partial metric space. The paper includes five chapters.The first chapter as an introduction, introducing the background of contractive type maps on quasi-partial metric space and the present situation, giving the research work and results of this paper.In the second chapter, we give the definition of the quasi-partial Hausdorff metric and prove some properties of quasi-partial Hausdorff metric in quasi-partial metric space. We also use these properties to prove the fixed point theorems of the multi-valued mapping on quasi-partial metric space.In the third chapter, we generalized the properties of the contractive maps on the base of the present results of the Fixed point theorems for the contractive maps on partial metric spaces, and we also use these properties proved the fixed point theorems of generalized contractions on quasi-partial metric spaces.In the fourth chapter, we introduced the concept of weak a-contraction type maps, and established some new fixed point theorems for these maps.Finally, the conclusion is showed in the fifth chapter, and some problems we need to study later are given.