The Common Fixed Point Theorem Satisfying ?-Contraction And Generalized Cyclic Contraction On B₂-metric Space

Banach fixed point theorem is one of the most basic theoretical tools in fixed point theory.In essence,this principle is a typical fixed point theorem of algebraic type,through such a theorem,not only an iterative sequence can be constructed,but also existence and uniqueness of fixed points are obtained.After this principle was put forward,it began to gradually become the research interest of domestic and foreign scholars,and significant progress has been achieved.Several scholars introduced the generalized contract conditions and get the corresponding fixed point theory through improving the contract conditions in metric spaces;Some scholars got new theory through the study of the promotion of space;Some scholars generalized the mapping to three-variable even multivariate function and thus gained new fixed point theory.In recent years,one of the recently popular topics in fixed point theory is to show the existence of fixed point theorem in b2-metric space.In this paper,we use the given contractive conditions to construct the Cauchy Sequence on b2-metric space,and then use the related conditions and completeness of spaces to obtain the limits of the sequence.Finally,we prove that the unique limit is the point of coincidence or common fixed points of the given mappings.The full text is divided into four parts.First chapter,we introduced the origin of the b2-metric space and the basic concept of required in the full text.The second chapter,we discussed the existence problems of common fixed points for two mappings satisfying two different p-contractive conditions on b2-metric spaces,and provide the corresponding fixed point theorems.On the other hand,we also dis-cussed the problems of a group of common fixed point of mapping under the condition of contract.The third chapter,we discussed the existence problem of common fixed points for two mappings satisfying generalized cyclic contractive conditions on b2-metric spaces and the promotion of the theorem.The fourth chapter,we present a summary of the full text.The obtained results in this paper generalized and improve the corresponding conclusions in references and their relevant papers.