Geodesic
The Topological Degree of A-Proper Maps
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 403-412

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Wong, H. Ship Fah. The Topological Degree of A-Proper Maps. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 403-412. doi: 10.4153/CJM-1971-042-5
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