## Abstract and Applied Analysis

### Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces

Tomonari Suzuki

#### Abstract

One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let $C$ be a bounded closed convex subset of a Hilbert space $E$, and let $\{T(t): t \in \mathbb{R}_+ \}$ be a strongly continuous semigroup of nonexpansive mappings on $C$. Fix $u \in C$ and $t_1, t_2 \in \mathbb{R}_+$ with $t_1 \lt t_2$. Define a sequence $\{ x_n \}$ in $C$ by $x_{n} =(1-\alpha_n)/(t_2-t_1)\int_{t_1}^{t_2} T(s) x_nds + \alpha_n u$ for $n \in \mathbb{N}$, where $\{ \alpha_n \}$ is a sequence in $(0,1)$ converging to $0$. Then $\{ x_n \}$ converges strongly to a common fixed point of $\{T(t): t \in \mathbb{R}_+ \}$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2006 (2006), Article ID 58684, 10 pages.

Dates
First available in Project Euclid: 30 January 2007

https://projecteuclid.org/euclid.aaa/1170202980

Digital Object Identifier
doi:10.1155/AAA/2006/58684

Mathematical Reviews number (MathSciNet)
MR2211674

Zentralblatt MATH identifier
1130.47036

#### Citation

Suzuki, Tomonari. Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces. Abstr. Appl. Anal. 2006 (2006), Article ID 58684, 10 pages. doi:10.1155/AAA/2006/58684. https://projecteuclid.org/euclid.aaa/1170202980

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