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1	On completeness of partial metric spaces, symmetric spaces and some fixed point results Aphane, Maggie 12 1900 (has links) 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. / Geography / Ph. D. (Mathematics) 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 514.325 Metric spaces Symmetric spaces Fixed point theory