Nearly Uniformly Noncreasy Property Of Orlicz Sequence Spaces

Functional analysis is an extremely important subject with a wide range of contents,Among them,Banach space theory is an important branch,Nearly Uniformly Noncreasy property is one of the important research contents of the geometric theory of Banach spaces,and it has been concerned by people.In order to better discuss the nearly uniformly noncreasy property,two new geometries are introduced in this paper,sub near uniformly convex and sub near uniformly smooth.And the Banach two branching principle is used in Orlicz space for the first time.The nearly uniformly noncreasy property of Orlicz sequence spaces with Orlicz norm and Orlicz Musielak-sequence spaces with Orlicz norm are given.The full text is divided into three parts as follows:Firstly,the first part mainly introduces the main purpose and significance of this research,as well as the current research background and status,and briefly introduces some Orlicz sequence spaces and research results related to nearly uniformly noncreasy property.Secondly,in the second part,we discuss the nearly uniformly noncreasy property of Orlicz sequence spaces with Orlicz norm,At first,we give the relationship between sub nearly uniformly convex and uniformly convex,and then get the sub nearly uniformly convex property in Orlicz sequence space with Orlicz norm,and then give the necessary and sufficient condition for Orlicz sequence space with Orlicz norm to be weak sequence complete,From this,we obtain the sub nearly uniformly smooth in Orlicz sequence space with Orlicz norm,and deduce the nearly uniformly noncreasy property of Orlicz sequence space with Orlicz norm.In the last part,the characterizations of sub nearly uniformly convex and sub nearly uniformly smooth in Orlicz Musielak-sequence spaces with Orlicz norm are given,and the necessary and sufficient conditions for nearly uniformly noncreasy property in Orlicz Musielak-sequence spaces with Orlicz norm are summarized.It is also proved that Orlicz Musielak-sequence space with Orlicz norm has nearly uniformly noncreasy which has weak fixed point property.