Approximation of Common Fixed Points of Pointwise Asymptotic Nonexpansive Maps in a Hadamard Space - Advances in Pure Mathematics

APM > Vol.2 No.6, November 2012

Advances in Pure Mathematics

Volume 2, Issue 6 (November 2012)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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

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DOI: 10.4236/apm.2012.26068 3,826 Downloads 7,028 Views Citations

Author(s)

Safeer Hussain Khan, H. Fukhar-ud-din

Affiliation(s)

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

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 $\sum ^{\infty}_{n=1}$ (C_n(x)-1)＜ $\infty$ 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

Share and Cite:

S. Khan and H. Fukhar-ud-din, "Approximation of Common Fixed Points of Pointwise Asymptotic Nonexpansive Maps in a Hadamard Space," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 450-456. doi: 10.4236/apm.2012.26068.

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