Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure
Year: 2013
Analysis in Theory and Applications, Vol. 29 (2013), Iss. 3 : pp. 255–266
Abstract
In this paper, we consider a countable family of surjective mappings $\{T_n\}_{n \in\mathbb{N}}$ satisfying certain quasi-contractive conditions. We also construct a convergent sequence $\{x_n\}_{n \in \mathbb{N}}$ by the quasi-contractive conditions of $\{T_n\}_{n \in\mathbb{N}}$ and the boundary condition of a given complete and closed subset of a cone metric space $X$ with convex structure, and then prove that the unique limit $x^{*}$ of $\{x_n\}_{n \in \mathbb{N}}$ is the unique common fixed point of $\{T_n\}_{n \in \mathbb{N}}$. Finally, we will give more generalized common fixed point theorem for mappings $\{T_{i,j}\}_{i,j \in \mathbb{N}}$. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2013.v29.n3.5
Analysis in Theory and Applications, Vol. 29 (2013), Iss. 3 : pp. 255–266
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Common fixed point the convex property cone metric space.