Weak and strong convergence theorems without some widely used conditions

We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fr�chet differentiable norm. ? 2010 Academic Publications.Scopu

A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.The author H. Fukhar-ud-din is grateful to King Fahd University of Petroleum and Minerals for supporting the research project IN121055 and the author A. Kalsoom is grateful to Higher Education Commission (HEC) of Pakistan for financial support during this research