Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings

In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.

Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings inCAT(0)Spaces

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework ofCAT(0)spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptoticallyϕ-Strongly Pseudocontractive Mappings

We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptoticallyϕ-strongly pseudocontractive mappings in a uniformly smooth Banach space.

Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature.