The Some Poperties Of Generalized Orlicz Sequence Spaces

According to the application of different fields, Orlicz spaces are generalized tovarious forms of space, which make the research of Orlicz spaces to be more theoret-ically significat and applicationally promising. From2008, Vakeel A Khan has gavesome forms of generalized Orlicz spaces, and investigated some basic properties ofthese spaces. Generalized Orlicz spaces will be summarized in this dissertation, andthree types of these generalized Orlicz sequence spaces will be studied.The main content is divided into the following several parts:The first chapter is introduction. Through analyzing the relevant domestic andforeign literatures and summarizing the theories and applications of Orlicz spaces, weintroduces briefly basic theories of generalized Orlicz sequence spaces which will bestudied in this dissertation, and obtain the necessities and important significance of theresearch of these spaces.In second chapter, we were investigated the proportion of generalized Orlicz sequ-ence space l(u,△,Φ, p,r). The definition of generalized Orlicz sequence spacel(u,△,Φ, p,r) is been given and the definition paranorm of this space is been introduc-e by using an Orlicz function sequence, discuss the changes of l(u,△,Φ, p,r) withthe changes of u,△,Φ, p,r and get some basic properties of the generalized Orliczsequencel u,△,Φ, p,r, one of which is this solid.In third chapter, we were investigated the proportion of generalized Orlicz sequen-ce space BV_σ(Φ, p,r). We introduce the definition of generalized Orlicz sequencespace BV_σ(Φ, p,r), by using an Orlicz function, on the basis of the space BV_σ, whichhas been given by Mursaleen.In fourth chapter, we were investigated the proportion of generalized Orlicz seq-uence space2BV_σ(Φ, p,r). Orlicz sequence space BV_σ(Φ, p,r) has been extendto BV_σ(Φ, p,r), we obtain some results such as inclusion relations in this space,but the results are diffienent from the corresponding results of generalized Orliczsequence spacesBV_σ.