|
|
| |
| ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES |
| |
Citation： |
ZENG Luchuan,YANG Yali.ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES[J].Chinese Annals of Mathematics B,2001,22(3):397~404 |
| Page view： 1214
Net amount： 752 |
Authors： |
ZENG Luchuan; YANG Yali |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.19801023) and the
Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions
of MOE, China. |
|
|
| Abstract： |
Let C be a nonempty bounded subset of a $p$-uniformly convex
Banach space $X$, and $T=\{T(t):t\in S\}$ be a Lipschitzian
semigroup on $C$ with $\lim_{n\rightarrow\infty}\limits\inf_{t\in
s}\limits|\|T(t)\||<\sqrt{N_p}$, where $N_p$ is the
normal structure coefficient of $X$. Suppose also there exists a
nonempty bounded closed convex subset $E$ of $C$ with the
following properties: (P$_1)x\in E$ implies $\omega_w(x)\subset E;$
(P$_2)T$ is asymptotically regular on $E$. The authors prove that
there exists a $z\in E$ such that $T(s)z=z$ for all $s\in S$.
Further, under the similar condition, the existence of fixed
points of Lipschitzian semigroups in a uniformly convex Banach
space is discussed. |
Keywords： |
Fixed points, Lipschitzian semigroups, Asymptotic regularity,
Normal structure coefficient, Asymptotic center |
Classification： |
47H10, 47H09, 47H20 |
|
|
Download PDF Full-Text
|
|
|
|
