Fixed Point Theorems For Several Kinds Of Mappings In Rectangular B-metric Spaces

The birth of the Banach Contraction Principle has made people perfectly solve a series of important application problems such as the existence theorem of implicit functions,which has caused great attention from the mathematicians at home and abroad and deep research on fixed point theory.A series of novel contraction mappings,non-expansive-type mappings and fixed point theorems have subsequently appeared,which have been successfully applied to many fields such as game theory,topology,economic equilibrium,optimal control,and differential equations.Fixed point theory has become an indispensable branch of modern mathematics.In this thesis,the fixed point properties of several types of mappings in rectangular b-metric spaces are studied,and the main contents are as follows:First of all,the research background and the development status at home and abroad of fixed point theory and metric spaces are introduced,which provide a correct direction for the research work of this thesis.Secondly,combining with the characteristics and properties of rectangular b-metric spaces,the Ekeland variational principle and the existence of fixed points of Ciric mappings in above spaces are given.The Ekeland variational principle and its proof are shown in a complete rectangular b-metric space,and the related results are used to obtain the generalized form of Caristi's fixed point theorem.Last but not least,the existence and uniqueness of fixed points of F-contraction mappings in a complete rectangular b-metric space are studied by using the Picard iterative method,which extend the related results given by Lukcacs and Kajanto.The existence and uniqueness of the common fixed point of the F-contraction mappings are also studied.In addition,we introduce the concept of weak well-posedness of the fixed point problem for mappings,and we study the weak well-posedness of the fixed point problem for F-contraction mappings in a complete rectangular b-metric space.