Fixed point theory in various generalized metric-type spaces.
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Date
2022
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Abstract
In the theory of fixed points, there are numerous articles dealing with generalization of
the basic Banach contraction mapping principle. There has been two lines of approach.
The first one is concerned with generalizations of the contractive conditions on the
mapping space. The other line of investigation deals with various generalizations of
the metric spaces and the results that can be obtained in these new frameworks, referred
to as metric-type spaces. In this thesis, we elected for the latter approach by providing
a more general framework for a b-metric space , G-metric space and S-metric space.
In this thesis, we proved that these new metric-type spaces equipped with various
contractions type mappings have unique fixed points and provide numerous examples
of each metric-type spaced mentioned.
Description
Doctoral Degree. University of KwaZulu-Natal, Durban.