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 - <p style="text-align: justify;">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 $\{x_n\}_{n \in \mathbb{N}}$ &nbsp;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.</p>