In this treatise the convergence of iterative algorithms for the solution of non-linear operator equations in complex linear topological spaces are studied from the point of view of fixed-point theorems in such spaces... It was felt that the concept of the Gâteaux differential is a more natural one to use in connection with linear topological spaces. The beauty of the developed technique we mentioned earlier is essentially due to the fact that we are considering spaces over the complex number field. The resulting convergence theorems have also the added advantage of imposing no conditions on the second or higher order differentials of the operator T, as would be the case in an obvious extension ( which was not written down) of Kantorovich's work to such real linear topological spaces. [...]
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.116539 |
| Date | January 1964 |
| Creators | Kotze, Wessel Johannes. |
| Contributors | Schwerdtfeger, H. (Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy. (Department of Mathematics. ) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: NNNNNNNNN, Theses scanned by McGill Library. |
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