Convergence Theorems of Fixed Points for Classes of Nonlinear Operator

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.

Autorentext

S. M. Altwqi, got his B. Sc. degree in Mathematics from sana'a University, Republic of Yemen in 2006, and his M.Sc. degree from Faculty of Science Assiut University, Egypt, in 2010. Now, he is studying a PhD degree at the Faculty of Science, University of Assiut, Egypt. The field study is the functional analysis.