一致凸空间中Lipschitz半群的非线性遍历收缩定理(英文)

Nonlinear Ergodic Retraction Theorem for Lipschitzian Semigroups in Uniformly Convex Spaces

设C是P一致凸Banach空间E的一个非空有界闭凸子集．在证明了C上自映象的Lipschitz半群的一个非线性遍历收缩定理的基础上，进一步给出了如此定理在Lp空间（1＜p＜∞）中的应用．

Let C be a bounded closed convex subset of a p- uniformly convex Banachspace E. We prove an existence theorem of nonlinear ergodic retractions forLipschitzian semigroups of self- mappings on C . Further, we give an application of sucha theorem in Lp (1 <p <+ ∞) spaces.