| In this paper,we generalize the b metric space,acquire some fresh theorems in the b2 metric space,create theαγ-b2 metric space as well as the orthogonal extended b2metric space,and examine the conditions for the existence of immutable mapping points in these spaces,as well as further apply these conclusions to for the purpose of proving the existence of common fixed points of multiple mappings.And the full paper consists of five chapters.Chapter 1 contains the research context and current status of this study,as well as the primary research questions,basic concepts,and relevant symbols.In Chapter 2,the existence and study of multiple mappings to fixed points in b2metric spaces are investigated by establishing generalized(φ,f)_λ-type extension con-ditions in b2 metric spaces and instances are given.Furthermore,the research on b2metric spaces is advanced by the chapter’s conclusions.In Chapter 3,a newαγ-b2 metric space is created in which compression conditions controlled by the functionβare introduced,Banach-type,Geraghty-type,Kannan-type,and Chatterjea-type compression conditions are generalized,and the existence and u-niqueness of the mapping’s fixed points are investigated in depth.In Chapter 4,the concept of extension is first presented on the basis of the b2metric space to form the extended b2 metric space,and subsequently the definition of orthogonality is launched to create a new space,the extended b2 metric space of orthog-onality,where non-linear operators in the extended Banach-type exist and are distinct,Geraghty-type,Kannan-type,Chatterjea-type,Kannan-type,as well as Chatterjea-type compressed conditional nonlinear operators for the existence and uniqueness of fixed points.The last chapter provides a summary of the paper’s research,innovations,and outlook. |
