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The Topological Degree of A-Proper Maps

Published online by Cambridge University Press:  20 November 2018

H. Ship Fah Wong
H. Ship Fah Wong*
Affiliation:
University of Warwick, Coventry, England
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Recently several fixed-point theorems have been proved for new classes of non-compact maps between Banach spaces. First, Petryshyn [15] generalized the concept of compact and quasi-compact maps when he introduced the P-compact maps and proved a fixed-point theorem for this class of maps. Then in [6], de Figueiredo defined the notion of G-operator to unify his own work on fixed-point theorems and that of Petryshyn. He also proved that the class of G-operators was a fairly large one.

We notice the following facts: (i) The essential idea in the above cases is that if certain finite-dimensional “approximations” of the map have fixed points, then the map has a fixed point; (ii) One of the tools used in proving fixed-point theorems in the finite-dimensional case is the Brouwer degree and its generalization to maps of the type Identity + Compact in [8].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 3 , June 1971 , pp. 403 - 412
Copyright
Copyright © Canadian Mathematical Society 1971

References

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