## Taiwanese Journal of Mathematics

### THE SET OF COMMON FIXED POINTS OF A ONE-PARAMETER CONTINUOUS SEMIGROUP OF NONEXPANSIVE MAPPINGS IS $F(\frac{1}{2} T(1) + \frac{1}{2} T(\sqrt{2}))$ IN STRICTLY CONVEX BANACH SPACES

Tomonari Suzuki

#### Abstract

In this paper, we prove the following. Let $E$ be a strictly convex Banach space. Let $\{ T(t) : t \geq 0 \}$ be a one-parameter strongly continuous semigroup of nonexpansive mappings on a subset $C$ of $E$. Then $\bigcap_{t \geq 0} F(T(t)) = F\left( \frac{1}{2} T(1) + \frac{1}{2} T(\sqrt{2}) \right)$ holds, where $F(T(t))$ is the set of fixed points of $T(t)$ for each $t \geq 0$.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 2 (2006), 381-397.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403831

Digital Object Identifier
doi:10.11650/twjm/1500403831

Mathematical Reviews number (MathSciNet)
MR2208273

Zentralblatt MATH identifier
1101.47044

#### Citation

Suzuki, Tomonari. THE SET OF COMMON FIXED POINTS OF A ONE-PARAMETER CONTINUOUS SEMIGROUP OF NONEXPANSIVE MAPPINGS IS $F(\frac{1}{2} T(1) + \frac{1}{2} T(\sqrt{2}))$ IN STRICTLY CONVEX BANACH SPACES. Taiwanese J. Math. 10 (2006), no. 2, 381--397. doi:10.11650/twjm/1500403831. https://projecteuclid.org/euclid.twjm/1500403831

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