Some Properties Related To N-inner Product Spaces

In this thesis, we mainly explore the2-normed type U-spaces, and uniform normal structure, normal structure and fixed pionts of n-Banach spaces, and dicuss the relationship between some convexties which we introduce in this thesis and the problems of fixed pionts in n-Banach spaces. In addition, we introduce the concept of n-inner-product spaces, obtain some property of n-inner-product spaces and some equivalent conditions between n-normed linear spaces and n-inner-product spaces.This thesis consists of three parts.Chapter one:In this chapter, we have proved the existence and uniqueness of the fixed point under the contractive mappings; and have given the conception of quasi-contractive mapping in n-norm space and proved the corresponding existence and uniqueness of the fixed point.Chapter two:In this chapter, further researches of the U-spaces have been carried out and the concept of2-normed type U-spaces has been introduced. We also demonstrate uniform normal structure and fixed point property in2-normed type U-spaces. Meanwhile, we discuss the relationship between2-normed type U-spaces and other convexity, and obtain some property of2-normed type U-spaces. Chapter three:In this chapter, we introduce the concept of n-inner-product spaces, obtain that some property of n-inner-product spaces and some equivalent conditions between n--normed linear spaces and n-inner-product spaces.