Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces
Lanping Zhu, Qianglian Huang, Xiaoru Chen · Fixed Point Theory and Applications · 2011
Abstract In this article, we introduce a new three-step iterative scheme for the mappings which are asymptotically nonexpansive in the intermediate sense in Banach spaces. Weak convergence theorem is established for this three-step iterative scheme in a uniformly convex Banach space that satisfies Opial's condition or whose dual space has the Kadec-Klee property. Furthermore, we give an example of the nonself mapping which is asymptotically nonexpansive in the intermediate sense but not asymptotically nonexpansive. The results obtained in this article extend and improve many recent results in this area. AMS classification: 47H10; 47H09; 46B20.