Convergence of an Iterative Method for Non-Lipschitzian Nonself-Mappings

Kamonrat Nammanee

Abstract

In this paper, we introduce an iterative method for approximating
a fixed point of asymptotically nonexpansive in the intermediate sense nonself-mapping in a uniformly convex Banach space. We establish some strong and weak convergence theorems. The results generalize the corresponding some results of Khan and Hussian [S.H. Khan, N. Hussian, Convergence theorems for nonself asymptotically nonexpansive mappings, Comput. Math. Appl. 55 (2008) 2544–2553] and many authors.