Abstract
We extend the results of Schu ['Iterative construction of fixed points of asymptotically nonexpansive mappings', J. Math. Anal. Appl. 158 (1991), 407-413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci-Mann iteration process[EQUATION PRESENTED] where is a monotone asymptotically nonexpansive self-mapping defined on a closed bounded and nonempty convex subset of a uniformly convex Banach space and is the Fibonacci integer sequence. We obtain a weak convergence result in , with <[CDATA[1<p<∞using a property similar to the weak Opial condition satisfied by monotone sequences.
| Original language | English |
|---|---|
| Pages (from-to) | 307-316 |
| Number of pages | 10 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 96 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Oct 2017 |
Bibliographical note
Publisher Copyright:© 2017 Australian Mathematical Publishing Association Inc.
Keywords
- Fibonacci sequence
- Mann iteration process
- Opial condition
- Phrases asymptotically nonexpansive mapping
- fixed point
- monotone Lipschitzian mapping
- uniformly convex Banach space
ASJC Scopus subject areas
- General Mathematics