Proceedings of the Centre for Mathematics and its Applications

Othogonality and fixed points on nonexpansive maps

Brailey Sims

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Abstract

The concept of weak- orthogonality for a Banach lattice is examined. A proof that in such a lattice non expansive self maps of a non empty weakly compact convex set have fixed points is outlined. A geometric generalization of weak- orthogonality is introduced and related to the Opial condition.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 178-186

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340113

Mathematical Reviews number (MathSciNet)
MR1009604

Zentralblatt MATH identifier
0687.47041

Citation

Sims, Brailey. Othogonality and fixed points on nonexpansive maps. Workshop/Miniconference on Functional Analysis and Optimization, 178--186, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988. https://projecteuclid.org/euclid.pcma/1416340113


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