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Int. Journal of Math. Analysis, Vol. 4, 2010, no. 15, 721 - 726

A Common Fixed Point Theorem in Cone Metric Spaces

Xianjiu Huang

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, Chuanxi Zhu

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and Xi Wen

Department of Mathematics, Nanchang University Nanchang, 330031, Jiangxi, P.R. China

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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...