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