Geometric Constant Of Banach Space And Application In Fixed Point Theory

Geometric constants have always been the focus of our concern, they play an important role in fixed point theory. In recent years, many scholars mainly use the relationship of geometric constants to seek the sufficient conditions for Banach space to have normal structure, which gives some sufficient conditions for Banach space to have fixed point property.Geometric constants of Banach space and application in fixed point theory is studied in this thesis. Contents of this thesis are divided into three parts. In the first part, the research background, the significance and the basic knowledge of Banach space are introduced, such as weak orthogonal coefficient, normal structure, DL condition, and D property. Through the literature, the development trend and the issues of the research direction are learned, which provides the precedent conditions for the thesis.In the second part, Zb(?)g anuconstant in Banach space is introduced. First, the relationship between Zb(?)g anuconstant and some other constants is discussed. Then, in terms of von Neumann-Jordan constant, the problem of parameterized and generalized Zb(?)g anuconstant is investigated, which generalizes some well-known results of Gao Ji and Saejung. Finally, the bounded estimate and exact value of Zb(?)g anuconstant for some exact Banach spaces are given.In the third part, the relationship between A₂ (X) constant, T ( X ) constant and some coefficients are discussed, which gives the sufficient conditions for Banach space to have normal structure. Then, the problem of the existence of fixed point for the multivalued nonexpansive mappings is considered. Some sufficient conditions for Banach space to satisfy DL condition or D property are given by the different relationship of constants.