The Properties And Applications Of Generalized Zbǎganu Constant In Banach Space

Banach space geometry theory,as an important research direction in the field of functional analysis,has been closely related to various branches of modern mathematics research so far,and its theory and application have been studied and discussed in large numbers.Among them,as the most important research content of Banach space geometry theory,the importance of fixed point theory is self-evident.At the same time,it also provides the research basis for many other branches of modern mathematics,opens up the research idea,and contains active and rich vitality.An important research tool for exploring Banach’s spatial geometry theory is geometric constants,whose values and functional relationships with different constants are used to describe the abstract geometric structure of space,so that the geometric properties are transformed from qualitative description to quantitative calculation.Therefore,for Banach’s theory of space geometry,the study of space geometry constant has important theoretical significance and practical value.First,this paper introduces a brand new constant in Banach space,called the generalized Zbǎganu constantC_Z^（p）（a,X）.The definition and equivalence of the new constant are put forward,and some properties of the new constant are analyzed.At the same time,we calculate in concrete space and study the properties of new constants in ultrapower space.Subsequently,we present several sufficient conditions for normal structure of a Banach space in terms of this new constant,the generalized James constant J（a,X）,the generalized García-Falset coefficient R（,1X）and the coefficient of weak orthogonality of Simsμ（X）.Thus,we obtain the conditions for the existence of the fixed point property and the corresponding inferences.In this paper,we expand the analysis and study of the generalized Zbǎganu constant,making the new constant more widely used in the normal structure and fixed point properties of Banach space,enrich the fixed point theory of Banach space,and make the generalized Zbǎganu constant have a broader research prospect.