| The fixed point theory plays an important role in many branches of modern mathematics,and many mathematical problems can be transformed into fixed point problems,so it is of great significance to study fixed point theory for the development of mathematics.Since Banach put forward the contraction principle in 1922,the fixed point theory has been further developed.Many authors have proposed generalized contraction mappings and obtained their fixed point theorems.With more and more research,contraction mappings and their research spaces have been more generalized.Based on these,this paper aims to construct more general contraction mappings that can unify others types of contraction mappings in the literatures,and study the existence and uniqueness of their fixed points.The first chapter introduces the research background and research progress of the fixed point theory,especially the Banach contraction principle,as well as the research objective and main work of this paper.The second chapter obtains the fixed point conclusions for several kinds of enriched contractions in Banach spaces.Some new definitions of contractions are established,and their fixed point theorems and Maia type fixed point theorems are proved by iterative method.The third chapter presents the common fixed point conclusions for several pairs of generalized enriched contractions in generalized convex metric spaces.In generalized convex metric spaces,some new pairs of contractions,namely pairs of generalized enriched contractions,are established.And their common fixed point theorems and related corollaries are obtained.Furthermore,the relationship between the constants and the convergence rate of sequence is obtained through simple numerical experiments.The fourth chapter summarizes the paper and looks forward to the further research for enriched contraction mappings. |
