Search: MSC category 47H20
( Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07] )
1. CMB 2011 (vol 55 pp. 15)
||Browder's Convergence for One-Parameter Nonexpansive Semigroups|
We give the sufficient and necessary conditions
of Browder's convergence theorem
for one-parameter nonexpansive semigroups
which was proved by Suzuki.
We also discuss the perfect kernels of topological spaces.
Keywords:nonexpansive semigroup, common fixed point, Browder's convergence, perfect kernel
2. CMB 2011 (vol 55 pp. 882)
||Equivalence of $L_p$ Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups|
$L_p$ stability and exponential stability are two important concepts
for nonlinear dynamic systems. In this paper, we prove that a
nonlinear exponentially bounded Lipschitzian semigroup is
exponentially stable if and only if the semigroup is $L_p$ stable
for some $p>0$. Based on the equivalence, we derive two sufficient
conditions for exponential stability of the nonlinear semigroup. The
results obtained extend and improve some existing ones.
Keywords:exponentially stable, $L_p$ stable, nonlinear Lipschitzian semigroups