An example for a one-parameter nonexpansive semigroup

Suzuki, Tomonari

Abstr. Appl. Anal., Tome 2005 (2005) no. 2, p. 173-183 / Harvested from Project Euclid

Résumé

We give one example for a one-parameter nonexpansive semigroup. This example shows that there exists a one-parameter nonexpansive semigroup $\{T(t): t\geq 0\}$ on a closed convex subset $C$ of a Banach space $E$ such that $\mathrm{lim}_{t\rightarrow\infty}\|({1}/{t})\int_0^t T(s)x ds -x \|=0$ for some $x \in C$ , which is not a common fixed point of $\{T(t): t\geq 0\}$ .

Publié le : 2005-04-28
Classification:

@article{1116340207,
     author = {Suzuki, Tomonari},
     title = {An example for a one-parameter nonexpansive semigroup},
     journal = {Abstr. Appl. Anal.},
     volume = {2005},
     number = {2},
     year = {2005},
     pages = { 173-183},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116340207}
}

Suzuki, Tomonari. An example for a one-parameter nonexpansive semigroup. Abstr. Appl. Anal., Tome 2005 (2005) no. 2, pp.  173-183. http://gdmltest.u-ga.fr/item/1116340207/