The Study Of Convexity And Fixed Point Problems In N-Banach Spaces

In this thesis, we mainly explore the convergence, convexity and fixed pionts of n-Banach spaces, and discuss the relationship between some convexties which we introduced and problems of fixed pionts in n-Banach spaces.This thesis consists of four parts.Chapter one: In this chapter, the basical definitions and necessary lemmas are introduced in n-Banach spaces.Chapter two: In this chapter, the results of 2-normed spaces accordin -g to reference [8] were generalized to n-Banach spaces. It is shown that the relations and basic properties of strong and weak convergence.Chapter three: In this chapter, we introduce some convexities in n-Banach spaces, and discuss the relationship between them. We give two necessary and sufficient conditions for n-Banach spaces to be uniformly convex spaces or strongly convex spaces. In addition, the structural theor -em of strongly convex n-Banach spaces which satisfies some conditions are obtained.Chapter four: In this chapter, two fixed piont theorems of contractive mapping are established in n-Banach spaces. The existence of fixed point and the structure of fixed point set in non-expansive mapping are discuss -ed.