Vol. 53, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Iterative techniques for approximation of fixed points of certain nonlinear mappings in Banach spaces

Robert L Thele

Vol. 53 (1974), No. 1, 259–266
Abstract

Let D be a closed convex subset of a Banach space X, let T : D D be nonexpansive (that is, TxTyxy for every x,y D), and let Fλ = λT + (1 λ)I, where λ (0,1) and I denotes the identity on D. Several authors have found conditions under which the sequences of iterates {Tnx}, or the sequences {Fλnx}, converge strongly or weakly to fixed points of T for all x D. In this paper we establish conditions under which the sequences {F12nx} converge strongly to fixed points of T for all x in a neighborhood of the fixed point set of T; furthermore, our theorems hold for classes of mappings T more general than the class of nonexpansive mappings.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 18 December 1972
Revised: 1 March 1974
Published: 1 July 1974
Authors
Robert L Thele