On completeness of partial metric spaces, symmetric spaces and some fixed point results
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Authors
Aphane, Maggie
Issue Date
2016-12
Type
Thesis
Language
en
Keywords
Metric space , Quasi metric space , Dislocated metric space , Partial metric space , TV S-cone metric space , TV S-partial cone metric space , dislocated cone metric space , Convergent sequence , Cauchy sequence , 0-Cauchy sequence , Convergence complete , Cauchy complete , 0-Cauchy complete , Contraction constant , Contraction map , Lipschitzian constant , Lipschitzian map , Fixed point , Metric type space , Dislocated metric type space , Partial metric type space , Symmetric space
Alternative Title
Abstract
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.
Description
Citation
Aphane, Maggie (2016) On completeness of partial metric spaces, symmetric spaces and some fixed point results, University of South Africa, Pretoria, <http://hdl.handle.net/10500/23223>