On The Coefficient Of Musielak-Orlicz Space Equipped With Orlicz Norm

With the rapid development of quantum theory,hydrodynamics and theoretical mechanics in modern physics,the rapid development of mathematical theory has been promoted Functional analysis is an efficient mathematical tool to solve physical problems.It is a mathematical discipline that integrates analytical theory,geometric methods and algebraic theoretical framework,in order to solve problems in many fields.Among them,Banach space geometry is an important branch of functional analysis,and has many important applications,such as fixed point theory,calculus,continuum mechanics,variational theory,approximation theory,quantum information,mathematical physics methods,quantum information and so on.It is a research field full of vitality.As we all know,the geometric theory of Banach space is abstract and complex.It is very difficult to describe its geometric structure intuitively and clearly.As a kind of Banach space,Musielak-Orlicz space not only provides theoretical basis and proof idea for the study of geometric theory of Bnanach space,but also has important application value.Geometric constant is a powerful tool to describe the geometric properties of Banach spaces.Convex coefficient is the most well-known geometric constant.It can characterize the convexity structure of general Banach unit sphere.This paper mainly studies the convex coefficients of Musielak-Orlicz space with Orlicz norm.Due to the complexity of Musielak-Orlicz spaces with Orlicz norm,it is very difficult to calculate the convex coefficients.By special treatment of strictly convex Musielak-Orlicz function,this paper gives the exact expression of the convex coefficients of the spaces,and also repairs the results of classical Orlicz spaces.