A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:246

Article

Kaczor, W ; Kuczumow, T ; Reich, S

关键词: almost convergence;    almost orbit;    asymptotically nonexpansive mapping;    fixed point;    mean ergodic theorem;    nonlinear semigroup;    the Kadec-Klee property;    uniformly convex Banach space;   

DOI  :  10.1006/jmaa.2000.6733

来源: Elsevier

【 摘 要 】

Let X be a uniformly convex Banach space such that its dual X* has the Kadec-Klee property, C a bounded closed convex subset of X, and F = {T(t): t is an element of [0, infinity)} a one-parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense. We show that every continuous almost orbit of F is weakly almost convergent to a common fixed point of F. A discrete version of our main result is also included. (C) 2000 Academic Press.

【 授权许可】

Free