The main purpose of this thesis is to establish the convergence theorems of fixed points for classes of nonlinear operators in difierent types of spaces such as normed spaces, Banach spaces, uniformly convex Banach spaces, and convex metric spaces. In Chapter 1, contains some fundamental concepts. In Chapter 2, we establish approximate common fixed points of three quasi-contractive operators on a normed space through an iteration process with errors. And we show that the Noor iteration converges faster than the Ishikawa and Mann iteration for the class of Zamfirescu operators. In chapter 3, we prove the convergence theorems for nonexpansive nonself mappings. In Chapter 4, we prove some strong and weak convergence theorems for generalized three step iterative scheme to approximate common fixed points of three asymptotically nonexpansive nonself mappings. In Chapter 5 we prove the convergence of the three-step iterative scheme for three mappings of asymptotically quasi-nonexpansive type in convex metric space.