Approximation of Common Fixed Points of Pointwise Asymptotic Nonexpansive Maps in a Hadamard Space

Safeer Hussain Khan, H. Fukhar-ud-din

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, KSA.
Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar.

DOI: 10.4236/apm.2012.26068                

Abstract

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (C_n(x)-1)＜ to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.

Keywords

Pointwise Asymptotic Nonexpansive Map; Common Fixed Point; Ishikawa Iteration Process; Strong Convergence; Weak Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

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