The purpose of the thesis is to study completeness of abstract spaces. In particular,
we study completeness in partial metric spaces, partial metric type spaces, dislocated
metric spaces, dislocated metric type spaces and symmetric spaces that are
generalizations of metric spaces. It is well known that complete metric spaces have
a wide range of applications. For instance, the classical Banach contraction principle
is phrased in the context of complete metric spaces. Analogously, the Banach's
xed point theorem and xed point results for Lipschitzian maps are discussed in
this context, namely in, partial metric spaces and metric type spaces. Finally, xed
point results are presented for symmetric spaces / Mathematical Sciences / Ph. D. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/23206 |
| Date | 10 1900 |
| Contributors | Moshokoa, Seithuti Philemon, Aphane, Maggie |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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