Int. Journal of Math. Analysis, Vol. 4, 2010, no. 15, 721 - 726
A Common Fixed Point Theorem in Cone Metric Spaces
Xianjiu Huang
3 3,2
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4
, Chuanxi Zhu
3
and Xi Wen
Department of Mathematics, Nanchang University Nanchang, 330031, Jiangxi, P.R. China
4
Department of Computer Sciences, Nanchang University Nanchang, 330031, Jiangxi, P.R. China
Abstract
In this paper, we prove a common fixed point theorem for a sequence of mappings in cone metric spaces. This result offers a generalization of Huang and Zhang’ theorem in [11]. An example to support our result is presented.
Mathematics Subject Classification: 54E40; 54E35; 54H25 Keywords: Cone metric spaces; Common fixed point; Sequence
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Introduction
The study of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity, for example see [1-5] and it has a wide range of applications in different areas such as nonlinear and adaptive control systems, parameterize estimation problems, fractal image decoding, computing magnetostatic fields in a nonlinear medium, and convergence of recurrent networks, see [6-10]. Recently, Huang and Zhang [11] have replaced the real numbers by ordering Banach space and define cone metric space. They have proved some fixed point theorems of contractive mappings on cone metric spaces. The study of fixed point theorems in such spaces is followed by some other mathematicians, see [12-15]. The aim of this paper
Project supported by the National Natural Science Foundation of China(10461007 and 10761007) and supported partly by the Provincial Natural Science Foundation of Jiangxi, China (2008GZS0076 and 2007GZS2051). 2 xjhuangxwen@163.com
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Xianjiu Huang, Chuanxi Zhu and Xi Wen
is to show a common fixed point theorem for a sequence of mappings in cone metric spaces. This theorem generalize the results of Huang and Zhang [11]. Consider with L. Huang and X. Zhang [11], the following...