Some Properities Ralated To N-Banach Spaces

k-strictly convex space and k-uniformly convex space is a veryimportant space in the study about Convexity in general normed spaces.This paper focuses on a number of the equivalent conditions and nature ofthe n-normed space k-uniformly convex and k-strict convexity, anddiscuss the relationship between n-metric spaces and n-Banach spaces.We prove the convergence theorems of Ishikawa iteration of nonexpansiv-e mapping in uniformly convex n-Banach space. This thesis consists offour parts.Chapter one: The basicaldefinitions and necessary lemmas are posedin this chapter.Chapter two: In this chapter, we introduce the notion of k-strictconvex-ity and k-uniform convexity in n-Banach spaces and obtainseveral charicteristic descriptions of k-strictly convex or k-uniformlyconvex n-Banach spaces.Chapter three: Linear space is a special kind of metric space, but themetric space is not a normed linear space in general. In this chapter, wediscuss the relationship between n-normed spaces and n-metric spaces.Chapter four: In this chapter, we prove the convergence theorems ofIshikawa iteration for nonexpansive mapping in a uniformly convex n-Ba-nach space.