## Taiwanese Journal of Mathematics

### Common Fixed Points of a Finite Family of Nonself Generalized Asymptotically Quasi-Nonexpansive Mappings

Shuechin Huang

#### Abstract

Suppose that $C$ is a nonempty subset of a real Banach space $X$. In this article, we construct two types of iterative schemes with errors for a finite family $\{T_i\}_{i=1}^k$ of nonself generalized asymptotically quasi-nonexpansive mappings of $C$ into $X$. Furthermore, not only a necessary and sufficient condition for $\{x_n\}$ generated by each of those iterations to converge to a common fixed point of $\{T_i\}_{i=1}^k$ is obtained, but also the weak and strong convergence theorems of $\{x_n\}$ in uniformly convex Banach spaces are established as well.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 745-772.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406233

Digital Object Identifier
doi:10.11650/twjm/1500406233

Mathematical Reviews number (MathSciNet)
MR2810180

Zentralblatt MATH identifier
05954243

#### Citation

Huang, Shuechin. Common Fixed Points of a Finite Family of Nonself Generalized Asymptotically Quasi-Nonexpansive Mappings. Taiwanese J. Math. 15 (2011), no. 2, 745--772. doi:10.11650/twjm/1500406233. https://projecteuclid.org/euclid.twjm/1500406233

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