arrow
Volume 29, Issue 3
Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure

Y. J. Piao & H. Nan

Anal. Theory Appl., 29 (2013), pp. 255-266.

Published online: 2013-07

Export citation
  • 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.

  • AMS Subject Headings

47H05, 47H10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{ATA-29-255, author = {}, title = {Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n3.5}, url = {http://global-sci.org/intro/article_detail/ata/5061.html} }
TY - JOUR T1 - Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure JO - Analysis in Theory and Applications VL - 3 SP - 255 EP - 266 PY - 2013 DA - 2013/07 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n3.5 UR - https://global-sci.org/intro/article_detail/ata/5061.html KW - Common fixed point, the convex property, cone metric space. AB -

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.

Y. J. Piao & H. Nan. (1970). Common Fixed Points for a Countable Family of Quasi-Contractive Mappings on a Cone Metric Space with the Convex Structure. Analysis in Theory and Applications. 29 (3). 255-266. doi:10.4208/ata.2013.v29.n3.5
Copy to clipboard
The citation has been copied to your clipboard