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

✍ Scribed by Wiesława Kaczor; Tadeusz Kuczumow; Simeon Reich

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 378 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00392-3

✦ Synopsis

Let (X) be a uniformly convex Banach space such that its dual (X^{*}) has the KadecKlee property, (C) a bounded closed convex subset of (X), and (T: C \rightarrow C) a mapping which is asymptotically nonexpansive in the intermediate sense. We prove that every almost orbit of (T) is weakly almost convergent to a fixed point of (T).